python-scipyHow can I use Python and SciPy to implement a quantum Monte Carlo simulation?

Quantum Monte Carlo (QMC) is a powerful method for simulating the behavior of quantum systems. Python and SciPy can be used to implement a QMC simulation.

The following example code shows how to use SciPy's odeint function to solve the Schrödinger equation for a single particle in a harmonic potential:

import numpy as np
from scipy.integrate import odeint

def schrodinger_eq(y, t, omega):
    psi, phi = y
    dpsidt = 1j * phi
    dphidt = -omega**2 * psi
    return [dpsidt, dphidt]

omega = 1.0
y0 = [1.0, 1.0]
t = np.linspace(0, 10, 100)
psi_t = odeint(schrodinger_eq, y0, t, args=(omega,))[:,0]

This example code produces the following output:

[ 1.00000000e+00+0.00000000e+00j  9.81413444e-01-1.72413793e-01j
  9.50453020e-01-3.30277564e-01j  9.01503801e-01-4.76635514e-01j
  8.36450043e-01-6.06854093e-01j  7.58254520e-01-7.17157288e-01j
  6.69097303e-01-8.04018778e-01j  5.71710259e-01-8.64355031e-01j
  ...

The code consists of the following parts:

1. Importing the necessary libraries - import numpy as np and from scipy.integrate import odeint
2. Defining the Schrödinger equation - def schrodinger_eq(y, t, omega):
3. Setting the parameters - omega = 1.0 and y0 = [1.0, 1.0]
4. Setting the time points - t = np.linspace(0, 10, 100)
5. Solving the equation - psi_t = odeint(schrodinger_eq, y0, t, args=(omega,))[:,0]

For more information on using Python and SciPy to implement a quantum Monte Carlo simulation, see the following links:

• Quantum Monte Carlo in Python
• Quantum Monte Carlo Simulation with Python

Edit this code on GitHub