Lect_38_note

Lect_38_note - Chapter 40-42 Introduction to Quantum...

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Chapter 40-42 Introduction to Quantum Physics
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1D Schrödinger Equation U(x) 22 2 2 d ψ U ψ E ψ md x −+ = h z E is the energy of the particle z ψ ( x ) and d / dx must be continuous
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q V L/2 Wave Function of a Particle in a Box with Step Potential The particle can enter the forbidden region. -q
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A classic particle cannot enter the forbidden region. v H ½m v 2 =mg H
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v H ½m v 2 =mg H A quantum particle can enter the forbidden region.
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Barrier Potential q V L/2 d -q
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Schrödinger Equation q V L/2 22 2 2 d ψ U ψ E ψ md x + = h ψ (x) = 0 2 2 d ψ U ψ E ψ x −+ = h q V 2 2 d ψ U ψ E ψ x = h 0 d
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Wave Function of Barrier Potential q V L/2 d 1 ( x ) = A 1 sin kx 2 ( x ) = A 2 exp(- cx )
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Wave Function of Barrier Potential q V L/2 22 2 2 d ψ U ψ E ψ md x −+ = h 0 2 2 d ψ mE mE ψ k ψ where k dx =− = hh d ψ 3 ( x ) = A 3 sin kx + B 3 cos kx 1 ( x ) = A 1 sin kx 2 ( x ) = A 2 exp(- cx )
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Wave Function of Barrier Potential q V L/2 d ψ 3 ( x ) = A 3 sin ( kx + δ ) 1 ( x ) = A 1 sin kx 2 ( x ) = A 2 exp(- cx ) 2 2 22 d ψ mE mE ψ k ψ where k dx =− = hh
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Quantum Tunneling E < U -q Classic particle Quantum particle
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A classical lion A quantum lion
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This note was uploaded on 01/28/2011 for the course PHYS 011 taught by Professor Nianlin during the Fall '08 term at HKUST.

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Lect_38_note - Chapter 40-42 Introduction to Quantum...

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