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Plotting in Python: Contour Plot
Plotting in Python
Basic Plot and formatting
Subplot, Multiplot
Colormaps in Plots
Bar Plot
Pie Chart
Histogram
Quiver plot to show Vector Fields
Stream plot to Visualize Flow Data
Polar, Parametric Plot
Contour Plot
3D Plot
Density Plot
Animated Plot
Miscellaneous
Contour Plot: Program 1
2d Contour Plot of Gaussian Function
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # Define 2D Gaussian function Z = np.exp(-(X**2 + Y**2)) # Create contour plot plt.contour(X, Y, Z) plt.title('Contour Plot of 2D Gaussian Function') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 1
Contour Plot: Program 2
Contour Plot of Electric Potential in 2d
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-2, 2, 100) y = np.linspace(-2, 2, 100) X, Y = np.meshgrid(x, y) # Electric potential of a point charge k = 1 # constant r = np.sqrt(X**2 + Y**2) Z = k / r # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('Electric Potential of a Point Charge') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 2
Contour Plot: Program 3
Gravitational Potential Near a Massive Object
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # Gravitational potential (inverse square law) G = 6.67430e-11 # Gravitational constant M = 1.0 # Mass r = np.sqrt(X**2 + Y**2) Z = -G * M / r # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('Gravitational Potential Near a Massive Object') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 3
Contour Plot: Program 4
Wave Interference Pattern
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # Wave interference r1 = np.sqrt((X + 1)**2 + Y**2) r2 = np.sqrt((X - 1)**2 + Y**2) Z = np.sin(r1) + np.sin(r2) # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('Wave Interference Pattern') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 4
Contour Plot: Program 5
Quantum Harmonic Oscillator Probability Density
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # Probability density function Z = np.exp(-(X**2 + Y**2)) * (X**2 + Y**2) # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('Quantum Harmonic Oscillator Probability Density') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 5
Contour Plot: Program 6
2d Potential Well Contour
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # 2D potential well function Z = (X**2 + Y**2) # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('2D Potential Well Contour Plot') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 6
Contour Plot: Program 7
import numpy as np import matplotlib.pyplot as plt # Define grid x = np.linspace(-5, 5, 100) y = np.linspace(-5, 5, 100) X, Y = np.meshgrid(x, y) # Electric potential of a dipole r1 = np.sqrt((X + 1)**2 + Y**2) r2 = np.sqrt((X - 1)**2 + Y**2) Z = 1 / r1 - 1 / r2 # Create contour plot plt.contour(X, Y, Z, levels=50) plt.title('Electric Dipole Potential in 2D') plt.xlabel('X-axis') plt.ylabel('Y-axis') plt.colorbar() plt.savefig('plot.png')
Run Code
Output 7
Contour Plot: Program 8
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')
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Output 8
Contour Plot: Program 9
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')
Run Code
Output 9
Contour Plot: Program 10
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')
Run Code
Output 10