All Questions
Tagged with algorithms schroedinger-equation
3
questions
11
votes
1
answer
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Why use Crank-Nicolson over Matrix Exponential when solving Schrödinger's equation?
For Schrödinger's equation,
$$\psi(x,t+\Delta t)=e^{-i H\Delta t}\psi(x,t)\approx\frac{1-\frac{1}{2}i H\Delta t}{1+\frac{1}{2}i H\Delta t}\psi(x,t).$$
The right-most expression is the Crank-Nicolson ...
- 779
0
votes
0
answers
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Finding the initial state in the power method for Hamiltonian diagonalization
In section III of the lecture note Chapter 1: Exact Diagonalization, Weimer has described the Power method for Hamiltonian diagonalization.
The process requires the choice of an random initial state ...
- 422
2
votes
1
answer
342
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Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?
Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
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