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:
- Importing the necessary libraries -
import numpy as np
andfrom scipy.integrate import odeint
- Defining the Schrödinger equation -
def schrodinger_eq(y, t, omega):
- Setting the parameters -
omega = 1.0
andy0 = [1.0, 1.0]
- Setting the time points -
t = np.linspace(0, 10, 100)
- 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:
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