# Quantum Harmonic Oscillator in 1-D¶

sympy.physics.qho_1d.E_n(n, omega)[source]

Returns the Energy of the One-dimensional harmonic oscillator

n
the “nodal” quantum number
omega
the harmonic oscillator angular frequency

The unit of the returned value matches the unit of hw, since the energy is calculated as:

E_n = hbar * omega*(n + 1/2)

Examples

>>> from sympy.physics.qho_1d import E_n
>>> from sympy import var
>>> var("x omega")
(x, omega)
>>> E_n(x, omega)
hbar*omega*(x + 1/2)

sympy.physics.qho_1d.psi_n(n, x, m, omega)[source]

Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.

n
the “nodal” quantum number. Corresponds to the number of nodes in the wavefunction. n >= 0
x
x coordinate
m
mass of the particle
omega
angular frequency of the oscillator

Examples

>>> from sympy.physics.qho_1d import psi_n
>>> from sympy import var
>>> var("x m omega")
(x, m, omega)
>>> psi_n(0, x, m, omega)
(m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))


Pauli Algebra

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Quantum Harmonic Oscillator in 3-D