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Math Help - Wave Func.

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    Wave Func.

    The ground state (un-normalized) wave function of a given particle is described by:

    \psi_0(x) = e^{\frac{-\alpha^4x^4}{4}} with eigenvalue E_0 = \frac{h^2\alpha^2}{m}. Determine what the potential is when the particle moves.

    The book says the answer is:

    V(x)= (1/2m)(h/2pi)^2 alpha^2{(alpha^6)(x^6)-3(alpha^2)(x^2)
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  2. #2
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    Quote Originally Posted by DiscreteW View Post
    The ground state (un-normalized) wave function of a given particle is described by:

    \psi_0(x) = e^{\frac{-\alpha^4x^4}{4}} with eigenvalue E_0 = \frac{h^2\alpha^2}{m}. Determine what the potential is when the particle moves.

    The book says the answer is:

    V(x)= (1/2m)(h/2pi)^2 alpha^2{(alpha^6)(x^6)-3(alpha^2)(x^2)
    Substitute the given wave function and energy eigenvalue into the 1-d Schroedinger Equation and solve for V.
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