Quantum Harmonic Oscillator in 1-D¶
- sympy.physics.qho_1d.E_n(n, omega)[source]¶
Returns the Energy of the One-dimensional harmonic oscillator.
- Parameters
``n`` :
The “nodal” quantum number.
``omega`` :
The harmonic oscillator angular frequency.
Notes
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.abc import x, omega >>> E_n(x, omega) hbar*omega*(x + 1/2)
- sympy.physics.qho_1d.coherent_state(n, alpha)[source]¶
Returns <n|alpha> for the coherent states of 1D harmonic oscillator. See https://en.wikipedia.org/wiki/Coherent_states
- Parameters
``n`` :
The “nodal” quantum number.
``alpha`` :
The eigen value of annihilation operator.
- sympy.physics.qho_1d.psi_n(n, x, m, omega)[source]¶
Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.
- Parameters
``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.abc import m, x, omega >>> psi_n(0, x, m, omega) (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))