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Summary: Physics 222, Modern Physics, Exam 2
NAME______________________________________
You are graded on your work, with partial credit where it is deserved.
Please be clear and well-organized in all your steps.
1. (15) Show that
! x,t( ) = e"ipx/!
e"iEt/!
satisfies the time-dependent Schrödinger equation for a free particle
i!
!" x,t( )
!t
= #
!2
2m
!2
" x,t( )
!x2
and obtain the energy E in terms of the momentum p .
(b) (5) Is this wave traveling in the positive or the negative x direction? Explain.
2. A 3d wavefunction for an electron in a hydrogen atom is
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