一维量子谐振子

sympy.physics.qho_1d.E_n(n, omega)

Returns the Energy of the One-dimensional harmonic oscillator.

参数:

n :

The "nodal" quantum number.

omega :

The harmonic oscillator angular frequency.

笔记

返回值的单位与hw的单位相匹配，因为能量计算如下：

E_n=hbar 欧米茄 （n+1/2）

实例

>>> 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)

返回一维谐振子相干态的<n | alpha>。看到了吗https://en.wikipedia.org/wiki/concertive_状态

参数:

n :

The "nodal" quantum number.

alpha :

The eigen value of annihilation operator.

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

返回一维谐振子的波函数psi{n}。

参数:

n :

the "nodal" quantum number. Corresponds to the number of nodes in the wavefunction. n >= 0

x :

x coordinate.

m :

粒子的质量。

omega :

Angular frequency of the oscillator.

实例

>>> 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))