Question

Prove the following:

i. [AB,C] = [Â,C]B + Â[B,C]

ii. ihq = qH - Hq given that H = mq

Answer 1

(i)

$$[AB,C]=ABC-CAB$$

$$=ABC-ACB+ACB-CAB$$

$$=A(BC-CB)+(AC-CA)B$$

$$=A[B,C]+[A,C]B$$

(ii)

$$i\hbar \dot q=[q,H]=qH-Hq=q(mq)-(mq)q=0$$