Question

In class we solved the quantum harmonic oscillator problem for a diatomic molecule. As part of that solution we transformed coordinates from x, the oscillator displacement coordinate, to the unitless, y using the relationship where μ is the reduced mass of the diatomic molecule and k is the force constant. The solutions turned out to be: w(y)N,H, (y)e Where N is a normalization constant, H,(v) are the Hermit polynomials and v is the quantum number with values of v0,1,2,3,.. The first three wave functions are: Where the first bracketed term is N, the second term H(y), and e behavior of .(v) as y - +o assures correct a) First we will consider two interesting operators (ylowering operator y ) raising operator Where their names will become apparent shortly i) Determine the commutator for the two operators. Can they have simultaneous i) Apply (y + ^to ) Write your answer in terms of one of the wave functions times a constant

Answer 1

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