HW12 - PHYS851 Quantum Mechanics I, Fall 2008 HOMEWORK...

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PHYS851 Quantum Mechanics I, Fall 2008 HOMEWORK ASSIGNMENT 12 1. [20 pts] Using the recursion formula c j +1 = 2( + 1 + j n ) ( j + 1)( j + 2 + 2) c j and the other details from the series solution to the Hydrogen Radial Equation, compute the Radial wave functions: R 1 , 0 , R 2 , 0 , R 2 , 1 , R 3 , 0 , R 3 , 1 , and R 3 , 2 . Finding the normalization constant is not required. 2. [15 pts] Using the previous results, construct the fully-normalized wavefunctions: ψ 2 , 0 , 0 ( r,θ,φ ), ψ 2 , 1 , - 1 ( r,θ,φ ), ψ 2 , 1 , 0 ( r,θ,φ ) and ψ 2 , 1 , 1 ( r,θ,φ ). 3. [10 pts] Compute a R A and a R 2 A for the ground state of hydrogen. 4. [10 pts] Compute a X A and a X 2 A for the ground state of hydrogen. 5. [15 pts] What is the most probable radius for the ground-state of hydrogen? Based on the current model, what is the probability that the relative velocity in the ground state exceeds the speed of light? (Hint: use T = E V ( r ) and T = . 5 mv 2 to relate velocity to position.). Do the same for the
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This note was uploaded on 10/25/2010 for the course PHYSICS PHYS 851 taught by Professor Michaelmoore during the Fall '08 term at Michigan State University.

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