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Need help with this Harmonic Oscillator question, thanks

11.5.3 Coherent states 1. Calculate (zPz) and (z|H2|z) and derive the dispersions (11.39) mha Д,Н 3 һо\2] Д.Р3, (11.39) 2 The coherent state z) is an eigenvector of the (non-Hermitian) annihilation operator a with eigenvalue (212 = (2 expectation values: /2hmw Im z, (z|P|z) 〈z|비) = hw( |zl2 A coherent state |z) is defined as n) e-l2/2ea'z]0) = e 7/M21- n=0

Answer 1

a - mwx 2mwt a-a 2p Ca-a mk 2. (-) aat ata 2. 0 lear (ata(at-a) 2. t aaa a 2 ( f a <리군 그 4리0 1212 Lela ale as ela12 a27 lelp <리 14127 1-22 Scanedith CamScanner 2 +22 4

(2222 - 2atib 2 2ib= 2-2 b2-2 2 thw 21 - mwk 2. - -2 2 2리 + 2 mot 2- moh Proved H at 2 H a a t 4 eatal Leaa7 1212Le ata daaatal Gal+ 1) 간리

elH7 So, 4 +2121 cS Scanned with