Liboff Quantum Mechanics Solutions Pdf.zip -

[ \psi_n(x) = \left(\frac{m\omega}{\pi\hbar}\right)^{1/4} \frac{1}{\sqrt{2^n n!}} H_n(\sqrt{\frac{m\omega}{\hbar}}x) e^{-\frac{m\omega x^2}{2\hbar}} ]

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plt.plot(x, wavefunction) plt.title(f'Wavefunction of the Quantum Harmonic Oscillator for n={n}') plt.xlabel('Position') plt.ylabel('Wavefunction') plt.show() This example calculates and plots the wave function for the ground state ((n=0)) of a quantum harmonic oscillator. You can modify n to see the wavefunctions for different energy levels. # Example usage x = np

# Example usage x = np.linspace(-5, 5, 1000) n = 0 # Quantum number # Example usage x = np.linspace(-5

def harmonic_oscillator_wavefunction(n, x, m=1, omega=1, hbar=1): """ Compute the wave function of the quantum harmonic oscillator. Parameters: - n: quantum number - x: position array - m: mass - omega: angular frequency - hbar: reduced Planck constant Returns: - wavefunction at position x """ prefactor = (m*omega/(np.pi*hbar))**(1/4) / np.sqrt(2**n * np.math.factorial(n)) hermite_polynomial = hermite(n)(np.sqrt(m*omega/hbar)*x) exponential = np.exp(-m*omega*x**2/(2*hbar)) return prefactor * hermite_polynomial * exponential

wavefunction = harmonic_oscillator_wavefunction(n, x)