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Current File : /usr/lib/python3/dist-packages/sympy/physics/__pycache__/pring.cpython-310.pyc
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�8Va+�@s<ddlmZmZmZmZmZddlmZdd�Zdd�Z	dS)�)�sqrt�exp�S�pi�I)�hbarcCs.t|�t|�}}t|t|�tdt�S)a�
    Returns the wavefunction for particle on ring.

    Parameters
    ==========

    n : The quantum number.
        Here ``n`` can be positive as well as negative
        which can be used to describe the direction of motion of particle.
    x :
        The angle.

    Examples
    ========

    >>> from sympy.physics.pring import wavefunction
    >>> from sympy import Symbol, integrate, pi
    >>> x=Symbol("x")
    >>> wavefunction(1, x)
    sqrt(2)*exp(I*x)/(2*sqrt(pi))
    >>> wavefunction(2, x)
    sqrt(2)*exp(2*I*x)/(2*sqrt(pi))
    >>> wavefunction(3, x)
    sqrt(2)*exp(3*I*x)/(2*sqrt(pi))

    The normalization of the wavefunction is:

    >>> integrate(wavefunction(2, x)*wavefunction(-2, x), (x, 0, 2*pi))
    1
    >>> integrate(wavefunction(4, x)*wavefunction(-4, x), (x, 0, 2*pi))
    1

    References
    ==========

    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
           Mechanics (4th ed.).  Pages 71-73.

    �)rrrrr)�n�x�r�5/usr/lib/python3/dist-packages/sympy/physics/pring.py�wavefunctions)r
cCsJt|�t|�t|�}}}|jr!|dtdd||dStd��)a�
    Returns the energy of the state corresponding to quantum number ``n``.

    E=(n**2 * (hcross)**2) / (2 * m * r**2)

    Parameters
    ==========

    n :
        The quantum number.
    m :
        Mass of the particle.
    r :
        Radius of circle.

    Examples
    ========

    >>> from sympy.physics.pring import energy
    >>> from sympy import Symbol
    >>> m=Symbol("m")
    >>> r=Symbol("r")
    >>> energy(1, m, r)
    hbar**2/(2*m*r**2)
    >>> energy(2, m, r)
    2*hbar**2/(m*r**2)
    >>> energy(-2, 2.0, 3.0)
    0.111111111111111*hbar**2

    References
    ==========

    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
           Mechanics (4th ed.).  Pages 71-73.

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