Hi. I'm not too good at maths and I'm having some trouble figuring out the basics of what to do with complex conjugates of functions.(adsbygoogle = window.adsbygoogle || []).push({});

Our lecturer has set a couple problems requiring us to test if a few operators are Hermitian. Before I can get to those I thought I'd test the basic momentum operator: [tex](\frac{\hbar}{i} \frac{\partial}{\partial x})[/tex].

Using integration by parts:

[tex]\int_{-\infty}^\infty \Psi^\ast(x,t) (\frac{\hbar}{i} \frac{\partial}{\partial x}) \Psi(x,t) dx = \frac{\hbar}{i} [\Psi^\ast(x,t)\Psi(x,t)]^\infty_{-\infty} - \int_{-\infty}^\infty \Psi(x,t) (\frac{\hbar}{i} \frac{\partial}{\partial x}) \Psi^\ast(x,t) dx [/tex]

Now how do I deal with the first term? Does it reduce to 0 somehow? I recongnise that the second term should be equal to the LHS for the momentum operator to be shown as Hermitian.

Cheers. Kaan

EDIT: sorry, I found the answer https://www.physicsforums.com/showthread.php?t=138552"

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# Testing if the momentum operator is Hermitian

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