Lecture_21

Lecture_21 - PHYS 342 Fall Fall 2011 Lecture 21: The...

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PHYS 342 all 2011 Fall 2011 Lecture 21: The physics behind Pauli’s xclusion principle exclusion principle No two electrons in a quantum system can occupy the same quantum state on Reifenberger Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 21 1
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Why don’t electrons cascade into lowest energy state? p 5s 4d Carbon p 5s 4d Carbon s 3p 3d 4s 4p s 3p 3d 4s 4p ?? 2s 2p 3s ↑↓ ↑↓ 2s 2p 3s Why Not? 1s ↑↓ 1s ↑↓↑↓ ↑↓ Pauli’s Exclusion Principle (1925): No two electrons in a quantum system can occupy the same quantum state 2
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The physical origin of the Pauli Exclusion Principle The microscopic world is devoid of contrast. All electrons are the same, all protons are the same, etc. hese particles (all identical!) are described by avefunctions at These particles (all identical!) are described by wavefunctions that often overlap. Individual particles can be counted but cannot be distinguished. For this reason, at the microscopic level it is impossible to distinguish between the constituents. What does this imply? This simple fact presents a fundamental problem when we try to write a wavefunction for an N-particle system as a product of single particle wavefunctions: 2 2 1 1 ; ; . . . ) ..... ) N N r r r Co-ordinates of particle No. 1 22 11 ( ( (; ) .. ) () N n NN n n rr 3 Quantum numbers of particle No. 1
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; ; ) () ( ) ( ) r r r r r Consider the following wavefunction for N quantum particles This wavefunction implies that particle “1” has quantum numbers “n 1 and energy E 1 , that particle “2” has quantum numbers “n 2 ” and energy 12 11 22 (; ..... )( ) Nn n n N N rr  E 2 , etc. The FORM of the wavefunction implies there is a way to ISTINGUISH etween the various particles because DISTINGUISH between the various particles because……… n, , m , m s n, , m , m s n, , m , m s n, , m , m s B E 1 E 2 E 3 E N . . . . 3 N ou can e f o r e . . . . Simply interchanging particles 1&2 gives: You can see the difference! A f 4 3 N One click t e r
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For identical particles (like electrons), the situation is different ), u ff n, , m , m s n, , m , m s n, , m , m s n, , m , m s 123 N E 1 E 2 E 3 E N B e . . . .
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Lecture_21 - PHYS 342 Fall Fall 2011 Lecture 21: The...

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