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o

�8Va�	�@sDddlmZmZmZddlmZmZmZmZm	Z	dd�Z
dd�ZdS)�)�S�pi�Rational)�assoc_laguerre�sqrt�exp�	factorial�
factorial2cCs�tt||||g�\}}}}|d}td||tdd�d||dt|d�tt�td|d|d��}|||t||d�t|d|tj	d||d�S)aM
    Returns the radial wavefunction R_{nl} for a 3d isotropic harmonic
    oscillator.

    Parameters
    ==========

    ``n`` :
        The "nodal" quantum number.  Corresponds to the number of nodes in
        the wavefunction.  ``n >= 0``
    ``l`` :
        The quantum number for orbital angular momentum.
    ``nu`` :
        mass-scaled frequency: nu = m*omega/(2*hbar) where `m` is the mass
        and `omega` the frequency of the oscillator.
        (in atomic units ``nu == omega/2``)
    ``r`` :
        Radial coordinate.

    Examples
    ========

    >>> from sympy.physics.sho import R_nl
    >>> from sympy.abc import r, nu, l
    >>> R_nl(0, 0, 1, r)
    2*2**(3/4)*exp(-r**2)/pi**(1/4)
    >>> R_nl(1, 0, 1, r)
    4*2**(1/4)*sqrt(3)*(3/2 - 2*r**2)*exp(-r**2)/(3*pi**(1/4))

    l, nu and r may be symbolic:

    >>> R_nl(0, 0, nu, r)
    2*2**(3/4)*sqrt(nu**(3/2))*exp(-nu*r**2)/pi**(1/4)
    >>> R_nl(0, l, 1, r)
    r**l*sqrt(2**(l + 3/2)*2**(l + 2)/factorial2(2*l + 1))*exp(-r**2)/pi**(1/4)

    The normalization of the radial wavefunction is:

    >>> from sympy import Integral, oo
    >>> Integral(R_nl(0, 0, 1, r)**2*r**2, (r, 0, oo)).n()
    1.00000000000000
    >>> Integral(R_nl(1, 0, 1, r)**2*r**2, (r, 0, oo)).n()
    1.00000000000000
    >>> Integral(R_nl(1, 1, 1, r)**2*r**2, (r, 0, oo)).n()
    1.00000000000000

    ���)
�maprrrrrr	rr�Half)�n�l�nu�r�C�r�3/usr/lib/python3/dist-packages/sympy/physics/sho.py�R_nls00��@rcCsd||tdd�|S)aP
    Returns the Energy of an isotropic harmonic oscillator.

    Parameters
    ==========

    ``n`` :
        The "nodal" quantum number.
    ``l`` :
        The orbital angular momentum.
    ``hw`` :
        The harmonic oscillator parameter.

    Notes
    =====

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

        E_nl = (2*n + l + 3/2)*hw

    Examples
    ========

    >>> from sympy.physics.sho import E_nl
    >>> from sympy import symbols
    >>> x, y, z = symbols('x, y, z')
    >>> E_nl(x, y, z)
    z*(2*x + y + 3/2)
    rr)r)rr�hwrrr�E_nl@srN)�
sympy.corerrr�sympy.functionsrrrrr	rrrrrr�<module>s;

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