5 Solved Problems on the Quantum Mechanics l - Assignment 3 | PHY 389K, Assignments of Quantum Mechanics

Download 5 Solved Problems on the Quantum Mechanics l - Assignment 3 | PHY 389K and more Assignments Quantum Mechanics in PDF only on Docsity! Pye! of 2 Phys 384 KK HW 3 4 121186 1) Caleulate the Product Of the uneertanties of He esition and momentum opeyatar in the mixect afae W of fe energy loss ex Periment with CO molecules Aisewesed inclass (sect. I.9 ef beck aul HWI,|), 2) Obtain the prooluct of uncertainties AyP Aya fo any pure state of the oscillator d= =, Deni?) = 21) Gn, ae Zlanl®(nd)P coo Guat Comol the ueta fo etek AypP' dyp@ =™% 3.) A state |a} that obeys the equation Ala) = aa), where A is the harmonic oscillator annihilation op- + - 1 a erator, is called a coherent state. here Aandk A* denote the amhiletion aud creation (a) Show that the state fa) Where aq #3 ace Pléy nut ber es rarer, Jay=ce*o) wih ea F GAT cel, co «OMS (hy Calculate Hae eoustant C From Ila> l=! (normalization’: (c) Expand the state |x) in a series of eigenstatg, of the operator A*A, |), and use this to find the prob- ability that the coherent state contains n quanta. distribution is called a Poisson distribution. (a) Calculate (a|Mq), the average number of quanta in the coherent state, where N = A‘A. (2) Coleulate <ul@iay, <u] Ple>, <a] @?}e>, <a) P?le> (§) Calculate the uncertainty Aw, of the paorition 2 in He State |ou> anol He nuncer tainty Ans nih show that Aga? ot in he Steke le'> *) The probability Hat the lake [a> cowteinn n quande <1 gotta bg Kier!” pre proBabalaty do find the energy Ey an Me Coherent Slade 10>,