The raising (at) and lowering (a) operators of a harmonic oscillator satisfy the relations a/n >= √n|n-1 > and a+|n >= √n + 1/n · α +1|n+1>,n=1,2,3,... Obtain the matrix for a*.
The raising (at) and lowering (a) operators of a harmonic oscillator satisfy the relations a/n >= √n|n-1 > and a+|n >= √n + 1/n · α +1|n+1>,n=1,2,3,... Obtain the matrix for a*.
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Ass Q1: Quantum Mechanics
Question 1.3 please
Transcribed Image Text:Question 1
1.1
Evaluate the following:
(i)
SxSy + SySx
(ii)
S²S,³S²
(iii)
Use the concept of parity to show whether < 3p|xsinx|2s> is zero or not
1.2
Prove the following:
The scalar product is invariant under unitary transformation.
(ii)
The trace of a matrix in invariant under unitary transformation.
1.3
The raising (at) and lowering (a) operators of a harmonic oscillator satisfy the relations
a|n >= √nn - 1 > and a+|n > = √n + 1\n + 1 >, n = 1, 2, 3, ...
Obtain the matrix for at.
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