Quantum Harmonic Oscillator in 1-D¶
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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)
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sympy.physics.qho_1d.
coherent_state
(n, alpha)[source]¶ Returns <n|alpha> for the coherent states of 1D harmonic oscillator. See http://en.wikipedia.org/wiki/Coherent_states
n
- the “nodal” quantum number
alpha
- the eigen value of annihilation operator
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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))