- #1
ronaldoshaky
- 52
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Hello I am trying to find the probability density function for a particle in a potential well of a harmonic oscillator. (My question is about complex conjugates).
I know the formula. I have to multiply \Psi^{*} (x, t) \Psi (x, t)The wave function is a linear combination of stationary states, i.e.
\Psi (x, t) = \frac{1}{\sqrt{2}} [ \psi_{0} (x) e^{\frac{-i \omega_{0} t}{2}} + \psi_{1} (x) e^{\frac{- 3i \omega_{0} t}{2}} ]
\psi_{0} (x)and \psi_{1} (x) are real
the conjugates of \psi_{0} (x)and \psi_{1} (x) are
\psi_{0}^{*} (x)and \psi_{1}^{*} (x) but since the eigenfunctions are real (are the conjugates the same as the eigenfunctions), what happens when I multiply them together?
I thought that, for example,
\psi_{0}^{*} (x) \psi_{0} (x) = \psi_{0} (x) \psi_{0} (x)= |\psi_{0} (x) |^{2}
I know the formula. I have to multiply \Psi^{*} (x, t) \Psi (x, t)The wave function is a linear combination of stationary states, i.e.
\Psi (x, t) = \frac{1}{\sqrt{2}} [ \psi_{0} (x) e^{\frac{-i \omega_{0} t}{2}} + \psi_{1} (x) e^{\frac{- 3i \omega_{0} t}{2}} ]
\psi_{0} (x)and \psi_{1} (x) are real
the conjugates of \psi_{0} (x)and \psi_{1} (x) are
\psi_{0}^{*} (x)and \psi_{1}^{*} (x) but since the eigenfunctions are real (are the conjugates the same as the eigenfunctions), what happens when I multiply them together?
I thought that, for example,
\psi_{0}^{*} (x) \psi_{0} (x) = \psi_{0} (x) \psi_{0} (x)= |\psi_{0} (x) |^{2}
