Consider an operator A so that [A A] 1. (a) Evaluate the commutators [AA A] and [AA
Question:
Consider an operator A so that [A A†] 1.
(a) Evaluate the commutators [A†A A] and [A†A A†].
( b ) I f t h e a c t i o n s o f A a n d A † o n t h e s t a t e s a a r e g i v e n b y A a a a 1 a n d
A † a a 1 a 1 a n d i f a a a a , c a l c u l a t e a A a 1 , a 1 A † a a n d a A † A a a n d a A A † a .
(c) CalculateaAA†2 aandaAA†2 a.
Consider a two-dimensional space where a Hermitian operator A is defined by A 1 1 a n d A 2 2 ; 1 a n d 2 a r e o r t h o n o r m a l .
(a) Do the states 1 and 2 form a basis?
(b) Consider the operator B 1 2 . Is B Hermitian? Show that B 2 0.
(c) Show that the products B B † and B † B are projection operators.
(d) Show that the operator B B † B † B is unitary.
(e)Consider C BB†B†B. Show that C 11andC 22.
Mathematical Applications for the Management Life and Social Sciences
ISBN: 978-1305108042
11th edition
Authors: Ronald J. Harshbarger, James J. Reynolds