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Questions tagged [quantum-mechanics]

Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.

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Improving accuracy of Neural Network for determining qubit rotation angle using Mathematica

The physics example problem (to illustrate the use of a basic neural network using Mathematica) I am looking at is a qubit rotated about the y-axis, where the rotation angle is discretized as $\...
John Doe's user avatar
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using scipy.sparse.linalg.eigsh for degenerate states in Bose Hubbard model

I am currently writing a code for the Bose-Hubbard model, and I am calculating the ground states and single-particle density matrix for different values of U and J. As U=0, one would see how the ...
Lorenzo Carfora's user avatar
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How do you determine the Mott-Insulator to Superfluid transition in the Bose Hubbard System

I am doing some simulations on various systems expressed in 2nd quantization and one of the points of interest of mine was Phase transitions in the Bose-Hubbard model $$ H = \sum_{k} \{ t_k(b^\dagger_{...
Mephistopheles Faust's user avatar
1 vote
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Will hashing become vulnerable to quantum computers?

My knowledge of these subjects is reasonable but limited so please correct anything I say that is wrong. As I understand a hash, with today's technology, is virtually irreversible. Also, any good hash ...
Ethan's user avatar
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How can we symbolically working out $\phi^4$ theory green's function/propagator and consequences in python?

I am having some difficulty calculating Green's function symbolically in Python for $\phi^4$ theory. The specific rendition of the $\phi^4$ theory I have in mind can be written as follows. $\mathcal{L}...
cows's user avatar
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How can the current-voltage relationship of a series of tunneling junctions be most easily computed?

I'm working on a research project with my professor where we're trying to figure out how to determine the necessary semiconductor composition for a solar cell to have a particular bandgap in order to ...
Mikayla Eckel Cifrese's user avatar
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1 answer
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Is FDTD A Method for Simulating Quantum Field Theory for Photons?

I have been reading a bit about Quantum Field Theory and Photons, I read that the equation(s) for spin 1 massless particles (photons) in Quantum Field Theory are just Maxwell's Equations described in ...
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Can the Crank-Nicolson Method Be used to Solve The Schrodinger Equation with a Time Varying Potential?

I have been following an excellent article about how to use the Crank-Nicolson method to solve the Schrodinger equation. In the article, it starts with a $V(x, y, t)$ but the potential seems to become ...
cgbsu's user avatar
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Numerov Method with Time Varying Potential

Is it possible to use the Numerov method to solve the Time Dependent Schrodinger Equation ($\frac{i\partial\Psi(x, y, z, t)}{\partial t} = \nabla^2\Psi(x, y, z, t) + \Psi(x, y, z, t)V(x, y, z, t)$) ...
cgbsu's user avatar
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Simulating Quantum Wave Function/Schrodinger Equation With A Time Varying Potential

I have solved the Time Independent Schrodinger Equation using the Numerov method and diagonalizing the Hamiltonian, in 1 - 3 dimensions. I suppose I could time-evolve it by multiplying every element ...
cgbsu's user avatar
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Free Time Dependent Schrodinger Equation with Inhomogeneous Dirichlet boundary

There exists a FFT-based method to solve the poisson equation in inhomogeneous Dirichlet boundary condition using the sine-transform. For example, Which fourier series is needed to solve a 2D poisson ...
WhatsupAndThanks's user avatar
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Crank-Nicolson vs Spectral Methods for the TDSE

The time-dependent Schroedinger equation (TDSE) depends linearly on the system's initial state $\vert \psi(0) \rangle$, such that the solution can be generally written as $$ \vert \psi(t) \rangle = \...
QuantumBrick's user avatar
1 vote
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258 views

Monte Carlo simulation for the quantum oscillator in the path integral approach

The theory Consider a quantum harmonic oscillator described by the potential $V(q)=\frac{1}{2}m\omega^2 x^2$. In the path integral formulation, the partition function can be written as $$Z\propto\int ...
My Code is a Flying Circus's user avatar
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How to obtain the unitary operator to get specific partial trace using searching methods?

Is there a unitary $U_{AB}$ such that, for any density operator $\rho$, we have $${\rm {Tr}}_A \left[U_{AB} \left(\frac{I_A}{2} \otimes \rho_B\right)U_{AB}^{\dagger}\right]= \frac{\rho_B}{2}+\frac{I_B}...
Michael.Andy's user avatar
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Numerical solution to integro-differential equation

The time dynamics of an atom interacting with a reservoir of spectral density $J(\omega)$ are obtained by solving the following integro-differential equation: $$ \frac{\mathrm{d}c(t)}{\mathrm{d}t} = - ...
Angus's user avatar
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Problem with Time Evolving Block Decimation for small finite chains

Preliminary definitions: I have a code that uses TEBD (https://en.wikipedia.org/wiki/Time-evolving_block_decimation) to perform time evolution of a given Matrix Product State (MPS), lets call it $|\...
Zarathustra's user avatar
2 votes
1 answer
703 views

Solving the time dependent Schrödinger equation with leapfrog integration in 1D

To my frustration I am struggling to implement leapfrog integration for the time dependent Schrödinger equation. To the best of my knowledge this was first explicitly done in "A fast explicit ...
Martin C.'s user avatar
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How to get a Wannier function of tight-binding model numerically (i.e. Python)

I have a question on construction of a Wannier function for tight-binding model. Let's say we consider the tight-binding model of 1D chain with two atoms( site A and B in a unit cell). In k-space we ...
Ricky Pang's user avatar
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Solving the non-linear Hamiltonian using Scipy's root finding method

I am a complete novice to computational physics and am finding difficulty in implementing a code to iteratively solve for a $2\times2$ nonlinear Hamiltonian using Scipy's root solver. I can't seem to ...
hello_world30's user avatar
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Transparent Boundary Conditions for Finite Difference ADI PR 2D TDSE solution

I want to put (non-dirichlet) boundary conditions inside the code I wrote to solve the 2dim TDSE using the alternating direction implicit Peaceman - Rachford method. $$ (1 + iB\Delta t/2 ) \psi^{n+1/2}...
velenos14's user avatar
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1 answer
261 views

Schrodinger's Equation differential

I am working on a modified version of Schrodinger's equation (time-independent) where $\frac{d^2ψ}{dx^2}=-2(E-V)ψ$, where I have to consider $V = 0$ at all times. I have been asked to use Python in ...
Entangled Being's user avatar
3 votes
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157 views

Numerical calculation of out-of-time order correlators (OTOCs)

I want to numerically calculate OTOCs for different quantum mechanical systems. Consider the following Hamiltonian $$H=p_x^2+p_y^2+x^2y^2$$ and I want to calculate the following OTOC $$C_T(t)=-\left&...
ghost's user avatar
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1 answer
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Roothaan equations and Galerkin method

When we do Hartree-Fock computations by solving the Roothaan equations $FC = SC \varepsilon$ is it a Galerkin method?
tohoyn's user avatar
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1 answer
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Numerical Solution of the Schrödinger equation for hydrogen

I'm trying to solve the Schrödinger equation for the hydrogen atom in the following form numerically: $$\left[-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]R(r)=ER(r).$$ ...
mysterion123's user avatar
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95 views

Numerov method for 1D potential barrier problem: numerical errors

I wanted to solve a 1D potential barrier problem. It seemed easy enough to do: set a travelling wave coming from the left, part of it gets reflected by the barrier, and part of it gets gets ...
user3653831's user avatar
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1 answer
185 views

Computing eigenvalues of Schrodinger equation with spin

I want to solve a 2-dimensional particle in box problem with two electrons in the quantum well.I would like to take into account spin of electrons and Coulomb interactions to compute singlet and ...
celerion's user avatar
1 vote
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421 views

How to compute the Eigenvalue and Eigenstates of Quantum well with Effective mass using finite difference method in Python?

I want to compute the eigenvalues and eigenstates of a quantum well with different effective masses of electron in the barrier and in the quantum well. As can be seen [1]: https://github.com/mholtrop/...
celerion's user avatar
1 vote
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Weird behavior in for solving TISE in harmonic oscillator potential using the shooting method

I was solving the time independent Schrödinger equation using the shooting method for harmonic oscillator potential. This is the code that I wrote for that with the results (code is written in julia): ...
JaydevSR's user avatar
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1 answer
589 views

Numerical solution to the infinite well problem

I've used the following code to implement it ...
0-0's user avatar
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1 answer
180 views

Problems with the time-dependent Schrödinger equation solutions

I have this Mathematica problem that solves numerically the time-dependent Schrödinger equation in a box: ...
LongJohn's user avatar
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0 answers
607 views

Numerov method for solving Schrödinger equation

I have just begun learning computer science to apply it to Physics and I am trying to write a code for solving Schrödinger's equation of the harmonic oscillator (setting $V=\frac{x^2}{2}$) in one ...
Anna Stone's user avatar
2 votes
0 answers
92 views

Finding the extrema of a transition probability function for a quantum walker on a graph

The goal Implement some Python code to find the extrema points of a function that is strongly oscillating. The background Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
Optimus Prime Number's user avatar
3 votes
0 answers
158 views

Python routine to calculate shape resonances of H2

I am currently doing a project in which my aim is to write a program that can be used to calculate single and multi-channel shape resonances. So I'm looking at bound states and quasi-bound states. ...
Alon Shoshan's user avatar
2 votes
1 answer
257 views

A problem with Poisson equation

I'm computing the Hartree potentials of atoms by solving the Poisson equation and I use hydrogen atom as a test case. The Poisson equation for hydrogen atom in atomic units is given by $$\nabla^2 V_H =...
tohoyn's user avatar
  • 331
2 votes
1 answer
212 views

Why is Time evolving block decimation so efficient?

I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
Sito's user avatar
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2 votes
1 answer
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How can I evaluate more accurate energy eigenvalues from Schrodinger equation using shooting method?

I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...
Manas Dogra's user avatar
-1 votes
2 answers
528 views

2d Schrodinger Equation via matrix diagonalization in C

I am trying to solve the time-independent Schrodinger equation in two dimensions via discrete matrix diagonalization. I want the energy eigenvalues and the corresponding eigenfunctions for a given ...
user8384493's user avatar
-1 votes
1 answer
128 views

If not MATLAB, what software/programming language should I use to simulate/animate wave functions in various potentials + more? (example given)

I want to integrate programming into my learning in math and science in a very specific way. I want to create visualizations and simulations of concepts I am learning. When I learn a numerical method ...
Sean O'Gary's user avatar
1 vote
1 answer
481 views

Operator splitting to solve time dependent Schrödinger equation

I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
Sito's user avatar
  • 131
4 votes
2 answers
832 views

Numerical solution of zero-potential time-dependent Schrödinger equation in 1D

I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$ My issue is that I don't have the physical background to understand ...
VoB's user avatar
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4 votes
1 answer
509 views

Recommendation for a fixed-step ODE solver?

My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
pmu2022's user avatar
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2 votes
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Numerical integration of SDE: choice of $dt$ and algorithm

I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context: $$dX_{t} = a X_{t} dt + b X_{t} dW$$ where $X_{t}$ is my stochastic varible, $dt$ is my ...
Bruscaliffo's user avatar
3 votes
1 answer
367 views

Numerical solution to the Landau-Zener problem

I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a $2\times 2$ Hamiltonian $$\left(\begin{array}{c} \alpha t\\ \delta \end{...
Yuval Tamir's user avatar
2 votes
1 answer
413 views

Numerov method for Schrodinger equation

While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method. I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. ...
ben tenyson's user avatar
1 vote
1 answer
655 views

What will be the impact of quantum computing on existing numerical techniques (e.g. CFD)?

Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical ...
Time4Tea's user avatar
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1 vote
1 answer
379 views

How to do Weierstrass-transform in MATLAB?

I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform) on them. So I have the wave functions ($\Psi$), and the continuous ...
Zsombor's user avatar
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0 answers
499 views

Finding second excited state of Schrödinger equation with secant Runge Kutta method

In our assignment, we are required to find the energies of the ground state and the first two excited states of the Schrödinger equation in a harmonic potential: $$V = \frac{50 x^2}{(10^{-11})^2}\, .$...
Programmer's user avatar
1 vote
0 answers
128 views

How to numerically calculate the transition dipole integral in periodic systems?

Now I have wave functions $\psi_a$ and $\psi_b$ of two states in Gaussian CUBE format. I'd like to evaluate the transition dipole moment integral $\pmb\mu$ between these two states. As my simulation ...
Xiaoming Wang's user avatar
3 votes
1 answer
360 views

MATLAB: Faber approximation of the matrix exponential to solve Liouville-von-Neumann equation

EDIT: I moved the full code to my github page so the post can be read more easily. I am writing a script to take the Faber approximation approach outlined in Hassan Fahs paper (free access) and apply ...
Tony_V's user avatar
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2 votes
1 answer
648 views

Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
FeelsToWaltz's user avatar