Lecture12.pptx

Lecture12.pptx - 1 PHYS 360 Quantum Mechanics Mon Feb 7...

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Unformatted text preview: 2/7/11 1 PHYS 360 Quantum Mechanics Mon Feb 7, 2011 Lecture 12: The infnite square well: What can we do with a complete set o¡ wave ¡uncJons? Midterm Exam 1 is one week ¡rom today, Monday Feb 14. Closed book exam. Bring one sheet o¡ handwriUen notes. Covers everything through SecJon 2.2 (i.e. NOT the harmonic oscillator). Will give HW #4 later, not due unJl Monday Feb 21. − 2 2 m d 2 ψ n dx 2 + V ψ n = E n ψ n The Jme‐independent Schrödinger equaJon: Inside infnite square well V=0, so: − 2 2 m d 2 ψ n dx 2 = E n ψ n → d 2 ψ n dx 2 = − k n 2 ψ n , k n 2 = 2 mE n 2 Which o¡ these are valid eigen¡uncJons? 1. A sin( k n x ) 2. B cos( k n x ) 3. A sin( k n x ) + B cos( k n x ) 4. Dexp − i k n x + θ ( ) ⎡ ⎣ ⎤ ⎦ 5. all of the above N.b. e i θ = cos θ + i sin θ The equaJon ¡or the Jme‐dependence o¡ the wave¡uncJon: i 1 ϕ n d ϕ n dt = E n → d ϕ n dt = − iE n ϕ n Which o¡ these are valid eigen¡uncJons? 1. exp − iE n t / [ ] 2. cos E n t / ( ) 3. − i sin E n t / ( ) 4. all of the above Is it possible ¡or a purely real wave¡uncJon to solve the Jme‐dependent Schrödinger equaJon? 1. Yes 2. No i ∂Ψ ∂ t = − 2 m 2 ∂ 2 Ψ ∂ x 2 + V ( x , t ) Ψ THE Schrödinger EquaJon: Recap…....
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This note was uploaded on 04/23/2011 for the course PHYS 360 taught by Professor Durbin,stephen during the Spring '11 term at Purdue.

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Lecture12.pptx - 1 PHYS 360 Quantum Mechanics Mon Feb 7...

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