Program 1

Contour Plot

2d Contour Plot of Gaussian Function

Output 1

Program 2

Contour Plot

Contour Plot of Electric Potential in 2d

Output 2

Program 3

Contour Plot

Gravitational Potential Near a Massive Object

Output 3

Program 4

Contour Plot

Wave Interference Pattern

Output 4

Program 5

Contour Plot

Quantum Harmonic Oscillator Probability Density

Output 5

Program 6

Contour Plot

2d Potential Well Contour

Output 6

Program 7

Contour Plot

Output 7

Program 8

Contour Plot

Probability density of H like atom Contour Plot

import numpy as np
import matplotlib.pyplot as plt

# Constants
a0 = 1  # Bohr radius, set to 1 for simplicity (in atomic units)

# Define the radial wave function for hydrogen atom (n=1, l=0)
def hydrogen_wavefunction(r):
    return (1 / np.sqrt(np.pi * a0**3)) * np.exp(-r / a0)

# Define the probability density
def probability_density(r):
    psi = hydrogen_wavefunction(r)
    return np.abs(psi)**2

# Define grid in 2D (in x and y plane)
x = np.linspace(-5, 5, 200)
y = np.linspace(-5, 5, 200)
X, Y = np.meshgrid(x, y)

# Convert to radial coordinate r (since it's spherical symmetry, use r = sqrt(x^2 + y^2))
R = np.sqrt(X**2 + Y**2)

# Calculate the probability density
Z = probability_density(R)

# Plot the contour plot of the probability density
plt.contourf(X, Y, Z, levels=50, cmap='viridis')
plt.title('Probability Density of Electron in Hydrogen Atom (n=1, l=0)')
plt.xlabel('x (Bohr radii)')
plt.ylabel('y (Bohr radii)')
plt.colorbar(label='Probability Density')
plt.savefig('plot.png')
plt.show()

Output 8

Program 9

Contour Plot

Probability density of H like atom Contour Plot

import numpy as np
import matplotlib.pyplot as plt

# Constants
a0 = 1  # Bohr radius, set to 1 for simplicity (in atomic units)

# Define the radial wavefunction for n=2, l=1
def radial_wavefunction(r):
    return (1 / np.sqrt(24 * a0**3)) * (r / a0) * np.exp(-r / (2 * a0))

# Define the probability density
def probability_density(r, theta):
    R = radial_wavefunction(r)
    angular_part = np.cos(theta)**2  # Angular dependence for l=1, m=0
    return np.abs(R)**2 * angular_part

# Define grid in 2D (in x and y plane)
x = np.linspace(-10, 10, 200)
y = np.linspace(-10, 10, 200)
X, Y = np.meshgrid(x, y)

# Convert to radial coordinate r and angular coordinate theta
R = np.sqrt(X**2 + Y**2)
Theta = np.arctan2(Y, X)

# Calculate the probability density
Z = probability_density(R, Theta)

# Plot the contour plot of the probability density
plt.contourf(X, Y, Z, levels=50, cmap='plasma')
plt.title('Probability Density of Electron in Hydrogen Atom (n=2, l=1)')
plt.xlabel('x (Bohr radii)')
plt.ylabel('y (Bohr radii)')
plt.colorbar(label='Probability Density')
plt.savefig('plot.png')
plt.show()

Output 9

Program 10

Contour Plot

Probability density of H like atom Contour Plot

import numpy as np
import matplotlib.pyplot as plt

# Constants
a0 = 1  # Bohr radius, set to 1 for simplicity (in atomic units)

# Define the radial wavefunction for n=3, l=1 (3p orbital)
def radial_wavefunction_n3_l1(r):
    return (1 / (81 * np.sqrt(6 * a0**3))) * (6 - r / a0) * (r / a0) * np.exp(-r / (3 * a0))

# Define the radial wavefunction for n=3, l=2 (3d orbital)
def radial_wavefunction_n3_l2(r):
    return (1 / (81 * np.sqrt(30 * a0**3))) * (r / a0)**2 * np.exp(-r / (3 * a0))

# Define the probability density for n=3, l=1 (3p orbital)
def probability_density_n3_l1(r, theta):
    R = radial_wavefunction_n3_l1(r)
    angular_part = np.cos(theta)**2  # Angular dependence for l=1, m=0 (p-orbital)
    return np.abs(R)**2 * angular_part

# Define the probability density for n=3, l=2 (3d orbital)
def probability_density_n3_l2(r, theta):
    R = radial_wavefunction_n3_l2(r)
    angular_part = np.sin(theta)**2  # Angular dependence for l=2, m=0 (d-orbital approximation)
    return np.abs(R)**2 * angular_part

# Define grid in 2D (in x and y plane)
x = np.linspace(-15, 15, 300)
y = np.linspace(-15, 15, 300)
X, Y = np.meshgrid(x, y)

# Convert to radial coordinate r and angular coordinate theta
R = np.sqrt(X**2 + Y**2)
Theta = np.arctan2(Y, X)

# Calculate the probability density for n=3, l=1 (3p orbital)
Z_n3_l1 = probability_density_n3_l1(R, Theta)

# Calculate the probability density for n=3, l=2 (3d orbital)
Z_n3_l2 = probability_density_n3_l2(R, Theta)

# Plot the contour plot for n=3, l=1 (3p orbital)
plt.figure(figsize=(12, 6))

plt.subplot(1, 2, 1)
plt.contourf(X, Y, Z_n3_l1, levels=50, cmap='plasma')
plt.title('Probability Density for Hydrogen Atom (n=3, l=1, 3p)')
plt.xlabel('x (Bohr radii)')
plt.ylabel('y (Bohr radii)')
plt.colorbar(label='Probability Density')

# Plot the contour plot for n=3, l=2 (3d orbital)
plt.subplot(1, 2, 2)
plt.contourf(X, Y, Z_n3_l2, levels=50, cmap='viridis')
plt.title('Probability Density for Hydrogen Atom (n=3, l=2, 3d)')
plt.xlabel('x (Bohr radii)')
plt.ylabel('y (Bohr radii)')
plt.colorbar(label='Probability Density')

plt.tight_layout()
plt.savefig('plot.png')
plt.show()

Output 10

Plotting in Python

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot

Contour Plot