Did I find the right examples for you? yes no      Crawl my project      Python Jobs

All Samples(5)  |  Call(4)  |  Derive(0)  |  Import(1)
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``(more...)

        def psi_n(n, x, m, omega):
    """
    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))

    """

    # sympify arguments
    n, x, m, omega = map(S, [n, x, m, omega])
    nu = m * omega / hbar
    # normalization coefficient
    C = (nu/pi)**(S(1)/4) * sqrt(1/(2**n*factorial(n)))

    return C * exp(-nu* x**2 /2) * hermite(n, sqrt(nu)*x)
        


src/s/y/sympy-HEAD/sympy/physics/tests/test_qho_1d.py   sympy(Download)
from sympy import exp, integrate, oo, Rational, pi, S, simplify, sqrt
from sympy.abc import omega, m, x
from sympy.physics.qho_1d import psi_n, E_n
from sympy.physics.quantum.constants import hbar
 
    }
    for n in Psi:
        assert simplify(psi_n(n, x, m, omega) - Psi[n]) == 0
 
 
def test_norm(n=1):
    # Maximum "n" which is tested:
    for i in range(n + 1):
        assert integrate(psi_n(i, x, 1, 1)**2, (x, -oo, oo)) == 1
        for j in range(i + 1, n + 1):
            assert integrate(
                psi_n(i, x, 1, 1)*psi_n(j, x, 1, 1), (x, -oo, oo)) == 0