- #61
gracy
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Yup. First chapter is " The wave function" .BvU said:
Planar wave solution to zero potential Schrödinger equation
- Thread starter Schwarzschild90
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The discussion centers on solving the time-dependent Schrödinger equation for a free particle, where the potential V(x) is zero. The wave function is expressed as ##\psi(x, t) = e^{i(kx - \omega t)}##, leading to the relationship between wavenumber k and angular frequency ω. Participants explore the implications of complex coefficients in wave functions and the necessity to check that both ##e^{i(kx - \omega t)}## and ##e^{-i(kx - \omega t)}## satisfy the Schrödinger equation. There is a consensus that the original problem may contain errors, particularly in part (b), regarding the validity of certain wave functions as solutions to the equation. The conversation concludes with a discussion on the need for additional observables to distinguish between degenerate energy eigenstates in quantum mechanics.
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