HW2_Solutions

# HW2_Solutions - PHYS851 Quantum Mechanics I, Fall 2008...

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYS851 Quantum Mechanics I, Fall 2008 HOMEWORK ASSIGNMENT 2: Postulates of Quantum Mechanics 1. [10 pts] Assume that A | n ) = a n | n ) but that ( n | n ) negationslash = 1. Prove that | a n ) = c | n ) is also an eigenstate of A . What is its eigenvalue? What should c be so that ( a n | a n ) =1? Solution: A | a n ) = Ac | n ) = cA | n ) = ca n | n ) = a n ( c | n ) ) = a n | a n ) . ( a n | a n ) = | c | 2 ( n | n ) . Setting equal to unity requires c = radicalbig ( n | n ) . 2. [10 pts] Assume that | n ) and | a n ) are degenerate eigenstates of A with eigenvalue a n . They sat- isfy ( n | n ) = ( a n | a n ) = 1 and ( n | a n ) negationslash = 1. Show that the states | a n , 1 ) = | a n ) and | a n , 2 ) = | n )| a n )( a n | n ) ||| n )| a n )( a n | n )|| are both eigenstates of A with eigenvalue a n , and are mutually orthogonal. Now assume that the system is in state | ) when A is measured. Write an expression for the proba- bility to obtain the result a n . Write down the state of the system immediately after the measurement, assuming that a n was obtained by random chance....
View Full Document

## This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

### Page1 / 3

HW2_Solutions - PHYS851 Quantum Mechanics I, Fall 2008...

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

View Full Document
Ask a homework question - tutors are online