|Mar7-04, 03:27 AM||#1|
A tricky one...
What Unitary operator can transfer the ground state eigenfunction
f=1/sqrt(2*pi)*exp(-x^2/2) to the ground state eigenfunction of another harmonic oscillator f=1/sqrt(2*pi)*exp(-(x-d)^2/2)?
|Mar8-04, 09:41 AM||#2|
Your new wavefunction results from taking the original system and translating it in space. Therfore, you are looking for a translation operator. I am sure you must know which quantum observable acts as the generator of translations, so you just have to exponentiate that.
Here is a clue. Generally, spacetime symmetries lead to conserved quantitites and so translation invariance leads to the conservation of .....
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