130_notes.dvi

(Frankie) #1

  • O 1 ψ(x) = 1/ψ(x)

  • O 2 ψ(x) =∂ψ∂x(x)

  • O 3 ψ(x) =x^2 ψ(x)

  • O 4 ψ(x) =−ψ(x+a)




  1. For a free particle, the total energy operator H is given byH=p^2 / 2 m. Compute the commu-
    tators [H,x] and [H,p]. If a particle is in a state of definite energy, whatdo these commutators
    tell you about how well we know the particle’s position and momentum?




  2. Find the commutator [x,p^3 ].




  3. Compute the commutator [H,x^2 ] whereHis the Hamiltonian for a free particle.





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