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Numerical algorithms to generate a random wavefunction from a thermal ensemble
I am seeking an algorithm to generate a random wavefunction = $\sum {c_i |\varphi _i\rangle }$ from a thermal ensemble, whose density matrix $\rho \sim e^{-\beta H}$, without the need to diagonalize ...
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Solving Schrödinger's equation with Crank-Nicolson method
I am trying to numerically solve Schrödinger's equation with Cayley's expansion ($\hbar=1$)
$$\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 ...
