1. The creation and annihilation operatorsfor quantum harmonic oscillator satisfyâ¹|n) = √n + 1|n + 1),â |n) = √n|n - 1)for energy eigenstates [n) with energy En.Consider harmonic Oscillator withanharmonic perturbationHp² 11X4The following expressions are needed incalculating for the first order correction to2μ2 µ + z μw ² x ² + = μ w ² b²energy En. Verify each of these:a. (n|â¹²ââ¹|n) = 0b. (n|â¹â²â¹|n) = n(n + 1)

Answered: Image /qna-images/answer/2d957304-0aba-4822-a3c8-844e026cea0f.jpg

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)