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[A, A].

harmonic oscillator.

Ψ(x)= {Ncos(2πx/L) for -L/4≤x≤L/4

{0 otherwise

How to determine:

i) the normalisation constant N,

ii) the probability that the particle will be found between x=0 and x=L/8.

nontrivial commutation relations with the angular momentum operators. Use those relations to prove that A·B commutes with Jx, Jy, and

Jz.

variables L2 and Lz for the following orbital state functions:

(a) Ψ(x) = f(r) sin θ cos φ,

(b) Ψ(x) = f(r)(cos θ)2,

(c) Ψ(x) = f(r) sin θ cos θ sin φ.

Here r, θ, φ are the usual spherical coordinates, and f(r) is an arbitrary

radial function (not necessarily the same in each case) into which the

normalization constant has been absorbed

1. why can't we see matter as a particle and a wave?

2. use a similar example to explain the wave particle duality?