- #1
Happiness
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Suppose a wave function is a linear combination of 2 stationary states: ##\psi(x)=c_1\psi_1(x)+c_2\psi_2(x)##.
By [5.52] and [5.53], we have ##\psi(x+a)=e^{iK_1a}c_1\psi_1(x)+e^{iK_2a}c_2\psi_2(x)##. But to prove [5.49], we need ##K_1=K_2##. That means all the eigenvalues of the "displacement" operator D have to be the same. But why is it so?
Reference: Intro to QM, David J Griffiths, p224
By [5.52] and [5.53], we have ##\psi(x+a)=e^{iK_1a}c_1\psi_1(x)+e^{iK_2a}c_2\psi_2(x)##. But to prove [5.49], we need ##K_1=K_2##. That means all the eigenvalues of the "displacement" operator D have to be the same. But why is it so?
Reference: Intro to QM, David J Griffiths, p224