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Consider the square of the derivative operator D^2 (a) Show that D^2 is a linear operator (b) Find the eigenfunctions and corresponding eigenvalues of D^2. (c) Give an example of an eigenfunction of D^2 which is not an eigenfunction of D.
Unnormalized ground-state wavefunction of a particle
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Particle of mass m in a one-dimensional impenetrable box
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For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy. Prove that the first order energy correction vanishes for all n = odd integer excited state levels.
Please help me with this. I do not know how to do this. There is not even one example of doing these proofs in the book. The book just gives us these properties.
Momentum space representation of a wavefunction.
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Linearly independent and normalized degenerate eigenfunctions
I don't even know where to start with this problem. If someone could show this proof I would appreciate very much.
I'm looking at instructor notes for one of the problems in my textbook, the link is here: http://www.physics.smu.edu/~coan/hw_sols/5382/f02/5382_02_hw_sols_02.pdf On page (3), where it says "Part B" P'Max occurs when...., can you please explain to me how they got the equations directly below till the end of the Page (3).
Frequency shift in Compton scattering
How would one obtain the Compton shift equation if the incident photon and electron were moving in opposite directions to begin with?
