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Simultaneous observables for hydrogen
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[QUOTE="TSny, post: 4486492, member: 229090"] Hello. Something to think about. Should the z axis be special in the hydrogen atom? That is, if there exist states with definite non-zero eigenvalues of ##E, L^2,## and ##L_z##, why shouldn't there exist states with definite non-zero eigenvalues of ##E, L^2,## and ##L_x##? Suppose you had a wavefunction ##\psi(r, \theta, \phi)## that represents an eigenstate of ##E, L^2,## and ##L_z##. Can you think of how you could transform ##\psi(r, \theta, \phi)## into another function ##\psi'(r, \theta, \phi)##that would be an eigenstate of ##E, L^2,## and ##L_x## with the same eigenvalues for ##E## and ## L^2## and with an eigenvalue of ##L_x## equal to the eigenvalue that ##\psi## had for ##L_z##? [Edit: It might be easier to think in terms of Cartesian coordinates ##\psi(x, y, z)]## [/QUOTE]
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Simultaneous observables for hydrogen
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