{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exercise_Solution

# Exercise_Solution - Solution of the exercise in the Simple...

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

Solution of the exercise in the ‘Simple Harmonic Oscillator’: Most of you may have been familiar with the following relation: 1 1 1 1 | | | n n n x x a a x n n + + - - Φ = Φ = Φ , (1) So we could go further and get: ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 1 | | 1 1 2 1 2 2 1 1 2 n n n n n n x a x n a x n d m x dx x n m m d x x m dx n d m x x where d x n ϖ ϖ ϖ ϖ ϖ α α α + - + - - - - Φ = Φ = Φ - = Φ = - Φ = - Φ = h h h h h (2) Or equally we could rewrite the above result as: ( 29 ( 29 1 1 1 2 n n d y y y where y x dy n α - Φ = - Φ = (3) Go on to use this method you could finally obtain: ( 29 ( 29 ( 29 0 0 1/ 4 2 1/2 2 1/2 2 2 1 1 ! 2 1 1 exp 2 ! 2 exp 2 2 ! exp exp exp 2 2 2 ! n n n n n y n n n n d y y y dy n d m y y dy n n d y y dy n y d y y dy n ϖ π α π α π Φ Φ = - Φ ÷   = - - ÷ ÷ ÷   = - - ÷ ÷ ÷ = - - ÷ ÷ ÷ ÷ h 1 4 442 4 4 43 ( 29 2 1/2 2 2 2 2 exp exp exp 2 2 2 2 !

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.

{[ snackBarMessage ]}

### Page1 / 3

Exercise_Solution - Solution of the exercise in the Simple...

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

View Full Document
Ask a homework question - tutors are online