def harmonic_oscillator_V(x, m=1.0, omega=1.0, V_x0=0, x0=0):
    """returns the potential for the 1D Harmonic Oscillator,
    given the following inputs:
    INPUTS:
        x --> a numpy array
        m --> mass, defaults to atomic units
        omega --> oscillator frequency, defaults to atomic units.
        V_x0 --> Lowest value of potential (shift in y - axis), defaults to 0
        x0 --> x value where potential has a minimum

    """
    V_x = V_x0 + 1.0 / 2.0 * m * omega ** 2 * (x - x0) ** 2
    return V_x
