1 2. The harmonic oscillatorConsider the harmonic oscillator with classical angular frequency we, and mass m. By explicitintegration, together with the properties of Hermite polynomials Hn, show thatn +1Sin+121|x Pn (x) 41(x)dx =Si,n-1 +12mwcB =%3D-00Note that vou are not allowed to use the ladder operators.This expression is called the matrix element xmi of the harmonic oscillator.

To show the equation given above.

2. The harmonic oscillator Consider the harmonic oscillator with classical angular frequency we, and mass m. By explicit integration, together with the properties of Hermite polynomials Hn, show that 1 х ф, (х) ф.(х)dх%3D n+1 8Ln+1 mw. B = 81n-1 + Note that you are not allowed to use the ladder operators. This expression is called the matrix element xni of the harmonic oscillator.

2. The harmonic oscillator Consider the harmonic oscillator with classical angular frequency we, and mass m. By explicit integration, together with the properties of Hermite polynomials Hn, show that 1 х ф, (х) ф.(х)dх%3D n+1 8Ln+1 mw. B = 81n-1 + Note that you are not allowed to use the ladder operators. This expression is called the matrix element xni of the harmonic oscillator.