Questions tagged [quantum-mechanics]
Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.
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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 ...
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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}...
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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 ...
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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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Crank Nicolson Simulation Not Preserving Probability?
I have written a Crank-Nicolson simulation based on this post and the code it links too.
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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 ...
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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 ($\frac{i\partial\Psi(x, y, z, t)}{\partial t} = \nabla^2\Psi(x, y, z, t) + \Psi(x, y, z, t)V(x, y, z, t)$) ...
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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 ...
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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 ...
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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
$$ \vert \psi(t) \rangle = \...
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Monte Carlo simulation for the quantum oscillator in the path integral approach
The theory
Consider a quantum harmonic oscillator described by the potential $V(q)=\frac{1}{2}m\omega^2 x^2$. In the path integral formulation, the partition function can be written as $$Z\propto\int ...
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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
$${\rm {Tr}}_A \left[U_{AB} \left(\frac{I_A}{2} \otimes \rho_B\right)U_{AB}^{\dagger}\right]= \frac{\rho_B}{2}+\frac{I_B}...
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Numerical solution to integro-differential equation
The time dynamics of an atom interacting with a reservoir of spectral density $J(\omega)$ are obtained by solving the following integro-differential equation:
$$ \frac{\mathrm{d}c(t)}{\mathrm{d}t} = - ...
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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 $|\...
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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 ...
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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 ...
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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 ...
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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.
$$
(1 + iB\Delta t/2 ) \psi^{n+1/2}...
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Schrodinger's Equation differential
I am working on a modified version of Schrodinger's equation (time-independent) where $\frac{d^2ψ}{dx^2}=-2(E-V)ψ$, where I have to consider $V = 0$ at all times.
I have been asked to use Python in ...
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Numerical calculation of out-of-time order correlators (OTOCs)
I want to numerically calculate OTOCs for different quantum mechanical systems. Consider the following Hamiltonian
$$H=p_x^2+p_y^2+x^2y^2$$
and I want to calculate the following OTOC
$$C_T(t)=-\left&...
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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?
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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:
$$\left[-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]R(r)=ER(r).$$
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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 ...
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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 ...
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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/...
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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):
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Problems with the time-dependent Schrödinger equation solutions
I have this Mathematica problem that solves numerically the time-dependent Schrödinger equation in a box:
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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 ...
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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 ...
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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.
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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
$$\nabla^2 V_H =...
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Why is Time evolving block decimation so efficient?
I have a short question about Time evolving block decimation (TEBD). During a lecture I was told that this method is very efficient in evolving 1D quantum spin systems with only nearest neighbor ...
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How can I evaluate more accurate energy eigenvalues from Schrodinger equation using shooting method?
I am trying to use the "shooting method" for solving Schrodinger's equation for a reasonably arbitrary potential in 1D. But the eigenvalues so evaluated in the case of potentials that do not have hard ...
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2d Schrodinger Equation via matrix diagonalization in C
I am trying to solve the time-independent Schrodinger equation in two dimensions via discrete matrix diagonalization. I want the energy eigenvalues and the corresponding eigenfunctions for a given ...
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If not MATLAB, what software/programming language should I use to simulate/animate wave functions in various potentials + more? (example given)
I want to integrate programming into my learning in math and science in a very specific way. I want to create visualizations and simulations of concepts I am learning. When I learn a numerical method ...
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Operator splitting to solve time dependent Schrödinger equation
I encountered the split operator method to solve the time dependent Schrödinger equation during a lecture. I understand the method on a theoretical basis (I think at least), but I'm struggling to ...
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Numerical solution of zero-potential time-dependent Schrödinger equation in 1D
I want to solve numerically the one-dimensional time-dependent Schrödinger equation $$i \psi_t(x,t)=-\frac{\hbar}{2m} \psi''(x,t)$$
My issue is that I don't have the physical background to understand ...
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Recommendation for a fixed-step ODE solver?
My problem involves the solution of a second-order ODE with a fixed-step (input and output). Specifically, this ODE is the radial part of Dirac and Schrödinger equation for a spherical symmetric ...
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Numerical integration of SDE: choice of $dt$ and algorithm
I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context:
$$dX_{t} = a X_{t} dt + b X_{t} dW$$
where $X_{t}$ is my stochastic varible, $dt$ is my ...
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Numerical solution to the Landau-Zener problem
I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a $2\times 2$ Hamiltonian
$$\left(\begin{array}{c} \alpha t\\ \delta \end{...
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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. ...
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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 ...
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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 ...
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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}\, .$...
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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 ...
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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 ...
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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 ...
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Hydrogen-like wavefunction as starting guess for atomic solver?
I've been looking into radial solvers for quantum wave equations (Schroedinger and Dirac). In both cases, the suggestion seems to be to go with the "shooting method", with integration schemes of ...
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Double potential well with Python
I'm trying to understand the Schrödinger equation and solving it a bit better, and I'm running into some doubts while coding, even though I am adapting the code to this situation. Also I tried asking ...
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