Lecture11.pptx - 1/26/11 PHYS360QuantumMechanics...

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1 PHYS 360 Quantum Mechanics Fri Feb 4, 2011 Lecture 11: The infnite square well: What can we do with a complete set o± wave ±uncJons? 2 2 m d 2 ψ n dx 2 + V n = E n n The Jme‐independent Schrödinger equaJon: Inside infnite square well V=0, so: 2 2 m d 2 n dx 2 = E n n d 2 n dx 2 = k n 2 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 = cos + i sin The equaJon ±or the Jme‐dependence o± the wave±uncJon: i 1 ϕ n d n dt = E n d n dt = iE n 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…. The Infnite Square Well V x ( ) = 0, if 0 x a, , otherwise 2 2 m d 2 dx 2 + V n = E n n We will solve this equaJon frst outside the well, then inside, then match up the soluJons.
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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 University-West Lafayette.

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Lecture11.pptx - 1/26/11 PHYS360QuantumMechanics...

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