# Tag Info

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1 vote

### Can the Crank-Nicolson Method Be used to Solve The Schrodinger Equation with a Time Varying Potential?

Overview Quantum-mechanical time-evolution assigns to a given wavefunction at time $t_0$ a new one at time $t$ under preservation of the norm. Its action is thus expressed through a unitary time-...
• 3,177
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### Can the Crank-Nicolson Method Be used to Solve The Schrodinger Equation with a Time Varying Potential?

I suspect that section 3.3 of the following thesis may be what you're looking for: Numerical simulation of time-dependent quantum systems. Edit: As noted by "davidhigh" in another answer the ...
1 vote
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### FDM on nonlinear PDEs

It becomes a root finding problem. Find $u^{n+1}$ such that $$u^{n+1} + \Delta t \theta F(u^{n+1},t^{n+1}) = u^n + \Delta t (\theta - 1) F(u^{n},t^{n}).$$ Now, you can multiply by a test function, ...
• 2,821
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### Crank-Nicholson for diffusion-advection vs diffusion equation

Take the first expression and start to reduce the $x$ values to $x_i$, \begin{align} \frac{u_{i+1}^n - u_i^n}{x_{i+\frac{1}{2}}} - \frac{u_i^n - u_{i-1}^n}{x_{i-\frac{1}{2}}} &= \frac{(x_i-\...
• 6,109
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### Is the diffusion equation with Neumann and Dirichlet BCs well-posed?

Problem well posed Your problem is well posed. On the discretization with Crank-Nicholson I am not familiar with MMS, and I wonder how you got that ungeneralised form of the diffusion equation. ...
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### Solving an equation in space and time using the Crank-Nicolson approach

This question is confusing. At first you are speaking of a steady-state equation, and suddenly you speak of a time scale... I will try to clarify the following. From the numerical PDEs standpoint, ...
1 vote

### Numerical solution of non-linear heat-diffusion PDE using the Crank-Nicolson Method

Anyone still interested in an answer, see this article: P. Y. P. Chen and B. A. Malomed, "Lanczos-Chebyshev pseudospectral methods for wave-propagation problems," Mathematics Computers ...
1 vote

### How to handle boundary conditions in Crank-Nicolson solution of IVP-BVP?

Let me give an answer that is a general comment on prescribed zero flux for advection-diffusion (or convection-diffusion) PDE that is an important topic and it might be (but not necessary) the problem ...
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