quiz_matrix_operators

quiz_matrix_operators - Write down ψ(t"Bonus"...

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(Name optional: _____________________________) Physics 3220  "QUIZ"  ( Not for credit , just to learn from!) Start it on your own ....  Consider quantum states with definite angular momentum quantum number      l   =1.      There are just 3 basis states:  Y 1 1 , Y 1 0 , and Y 1 - 1 , or in Dirac notation, call them 1,1 , 1,0 , and 1,- 1 . Since  l =1 is throughout this entire problem, we will stop writing the leading  quantum number entirely, just to save time!  So  our three basis states are written simply as: 1 = 1 0 0 , 0 = 0 1 0 , - 1 = 0 0 1 A) How would you write the bra  0  in matrix notation? B) How would you write the operator L in this basis?   (It should be a matrix!)  C) How would you write the operator L z  in this basis? D) Suppose you start with  ψ ( t = 0) = 1 6 1 2 1 , and suppose also that the Hamiltonian is simply  H = L /2I      (where I is some given constant with appropriate units)   
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Unformatted text preview: Write down ψ (t): ("Bonus" questions on back, if you have time!) Bonus #1: Again, suppose we start with ψ ( t = 0) = 1 6 1 2 1 , but this time, what if the Hamiltonian is H = cL z (where c is some constant with appropriate units) Write down ψ (t): Bonus #2: The raising operator L + raises the m quantum number, which means L + m m +1 The proportionality constant is worked out in Griffiths Ch. 4 : L + m = h ( l-m )( l + m +1) m +1 i) How would you write the operator L + in the basis we're using in this problem? ii) Recall L- = (L + ) † Write the operator L- in matrix form. (This should be a quicky now!) CHECK: What do you expect to get for L-- 1 ? Does your matrix give you the right answer?...
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This note was uploaded on 02/27/2012 for the course PHYSICS 3220 taught by Professor Stevepollock during the Fall '08 term at Colorado.

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quiz_matrix_operators - Write down ψ(t"Bonus"...

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