- #1
Master J
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I have a rather fundamental question which I guess I've never noticed before:
Firstly, in QM, why do we define the expectation values of operators as integral of that operator sandwiched between the complex conjugate and normal wavefunction. Why must it be "sandwiched" like this?
From this comes my problem. In deriving an equation for current density, I multiplied the electron velocity, which is the momentum over mass, times the density, which is the wavefunction times its complex conjugate.
Yet I have noticed that in a text, the momentum operator is ALSO conjugated. That is to say, since the momentum involves a derivative, and I have a product of wavefunctions, I use the product rule, but the second term has ih d/dx instead of the usual -ih d/dx.
Can someone shed some light on this??
Firstly, in QM, why do we define the expectation values of operators as integral of that operator sandwiched between the complex conjugate and normal wavefunction. Why must it be "sandwiched" like this?
From this comes my problem. In deriving an equation for current density, I multiplied the electron velocity, which is the momentum over mass, times the density, which is the wavefunction times its complex conjugate.
Yet I have noticed that in a text, the momentum operator is ALSO conjugated. That is to say, since the momentum involves a derivative, and I have a product of wavefunctions, I use the product rule, but the second term has ih d/dx instead of the usual -ih d/dx.
Can someone shed some light on this??