0f61b683-46a0-4cfd-a65a-67c8f89ce7b6 15 6 9 decimal

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Hermite polynomials n x H 1 - (k^n! (* (k! (n 2 k * - (! (* / 2 x * (n 2 k * -^* (k 0 n 2 / Floor sum :

Normalised wave function n x Ψ 1 π / (14 /^12 n^n! (* sqrt / * n x H * x 2^- 2 / exp * :

01012 -^Ψ (2^0.56419

n 4 :

n x Ψ 2 ^

x V 12 / x 2^* : x Ψ.0 0 x Ψ (2^12 / + : x Ψ.1 1 x Ψ (2^32 / + : x Ψ.2 2 x Ψ (2^52 / + : x Ψ.3 3 x Ψ (2^72 / + : 51 line

plot x V x Ψ.0 x Ψ.1 x Ψ.2 x Ψ.3 51 sys :

plot

n x Ψ n x H x 2^- 2 / exp * :

Wave function for the harmonic oscillator

n x PDψ n x Ψ (2^:

Probanility densities of the eigenstates

n x Es n x Ψ (2^x * :

The expectation function

n x Es x 05 int 648

The expectation value

0 n x PDψ 2 1 sys 0 n x Es 2 1 sys