AnswerToTheTakeHomeQuiz2

AnswerToTheTakeHomeQuiz2 - PHY4221 Quantum Mechanics I...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHY4221 Quantum Mechanics I (Fall 2004) Take Home Quiz 2 (Answer) For simplicity, we have set 1 m = = = h . Thus the momentum and position operator could be written as: ( 29 ( 29 1 , 2 2 i x a a p a a + + = + =- (1) So the Hamiltonian could be expressed in terms of the raising and lowering operators: ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 1 2 4 1 2 1 4 p H x a a x a a a a x + + + =- = --- = - +--- (2) So we have: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 , 2 , 2 , 1 2 1 4 1 2 1 4 1 2 1 1 4 2 1 1 1 2 1 2 1 4 m n m n m n m n m n m n m n m n m n m n m n H a a a a x a a a a x n n n n n n n n n n + + + + +- +- = - +-- + = - +-- + + + = - +- - - + = - + + +-- + - (3) We have proved before that the eigen functions of harmonic oscillators have fixed parity (if you...
View Full Document

This note was uploaded on 12/10/2011 for the course PHYS 4221 taught by Professor Cflo during the Spring '11 term at CUHK.

Page1 / 3

AnswerToTheTakeHomeQuiz2 - PHY4221 Quantum Mechanics I...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online