Crank-Nicolson method#
The Crank-Nicolson method is a second-order implicit approach that combines the forward Euler method and its backward counterpart at the k and k+1 iterations, respectively. The approximation of the state at the `k`th iteration is expressed as
\[\left(\mathbb{I}+\frac{i\Delta t}{2}H\right)\psi_{k+1}=\left(\mathbb{I}-\frac{i\Delta t}{2}H\right)\psi_{k}.\]
Techniques for matrix inversion can be employed to solve the system of equations in its matrix-vector form.
Other methods, such as the conjugate gradient descent seemps.cgs.cgs() , can also be adapted for implementation within an MPO-MPS framework.
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Solve a Schrodinger equation using a fourth order Runge-Kutta method. |