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for de Broglie waves

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【3.6 particle in a box】<br />

a prticle trapped in a box = a standing<br />

wave.<br />

Ψmust be zero at the walls<br />

λ n =2L/n n=1,2,3……<br />

De <strong>Broglie</strong> wavelength of trapped<br />

particles.<br />

Figure3.10<br />

Wave functions of a particle trapped in a box L wi<strong>de</strong>.<br />

KE=1/2(mv 2 )=(mv) 2 /2m=h 2 /(λ 2 2m)<br />

∵λ n =2L/n<br />

KE+v=E n the energy <strong>for</strong><br />

13

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