Problem 3 14 A Prove The Following Commutator Identities A B C A C B C Aa C A B C A C B B 1 (145.67 KiB) Viewed 21 times
Problem 3 14 A Prove The Following Commutator Identities A B C A C B C Aa C A B C A C B B 2 (65.87 KiB) Viewed 21 times
Problem 3.14 (a) Prove the following commutator identities: [A + B.C] = [A.C] + [B.C]. [ÂÂ, Ĉ] =  [B, Ĉ] + [Â, Ĉ] B. (b) Show that [x", p] = ihnx"-1. (c) Show more generally that [f(x), p] = indf ih dx' for any function f(x) that admits a Taylor series expansion. (d) Show that for the simple harmonic oscillator [Â, â+] = ±hwa. [‚â+] Hint: Use Equation 2.54. (3.64) (3.65) (3.66) (3.67)
s, Equation 2.50 becomes Ĥ + 2' ħw = hw (â _â + - =/ ). 2 â_â+ = H = hw (2.53) (2.54)
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