Question

1. n) are harmonic oscillator energy eigenstates. 10). А[2)- (a) Find Alo), Áli), and A12). (Ans: Alo)-0. Α1) V211).) (b) Consider a quantum state given by where a is a real number with 0 a 1. Calculate (ψ1e1ψ) and 2a2)/2mu.) that Δ ris at its minimum. (Ans: (as)2-A(3-6a2 + 4a4)/2mw. ns: ha (1-a2)/mw. (c) Find (Ar)2ー(v' U)-(圳刘の2, what is the value of a such a = V3/2.)

Answer 1

al n Cose c n In-1 (11) A 2 11 2 oM 2h A+ ?尸 2 牙 IT -IN 2

2 a /2 mw 2nw da 2m 3-64 +104 2
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