1. The creation and annihilation operators for quantum harmonic oscillator satisfy â¹|n) = √n + 1|n + 1), â |n) = √n|n − 1) - for energy eigenstates In) with energy En. Consider harmonic Oscillator with anharmonic perturbation H = 2₁² + 1/² H² x ² + 1/{ Hw² = 1/2 z 6² The following expressions are needed in calculating for the first order correction to energy En. Verify each of these: a. (n|â¹²ââ†|n) = 0 b. (n|â¹â²â¹|n) = n(n+1)
1. The creation and annihilation operators for quantum harmonic oscillator satisfy â¹|n) = √n + 1|n + 1), â |n) = √n|n − 1) - for energy eigenstates In) with energy En. Consider harmonic Oscillator with anharmonic perturbation H = 2₁² + 1/² H² x ² + 1/{ Hw² = 1/2 z 6² The following expressions are needed in calculating for the first order correction to energy En. Verify each of these: a. (n|â¹²ââ†|n) = 0 b. (n|â¹â²â¹|n) = n(n+1)
Related questions
Question
100%
Transcribed Image Text:1. The creation and annihilation operators
for quantum harmonic oscillator satisfy
â¹|n) = √n + 1|n + 1),
â |n) = √n|n - 1)
for energy eigenstates [n) with energy En.
Consider harmonic Oscillator with
anharmonic perturbation
H
p² 1
1
X4
The following expressions are needed in
calculating for the first order correction to
2μ
2 µ + z μw ² x ² + = μ w ² b²
energy En. Verify each of these:
a. (n|â¹²ââ¹|n) = 0
b. (n|â¹â²â¹|n) = n(n + 1)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
