lecture 2 de broglie and schrodinger

7/25/2019 Lecture 2 de Broglie and Schrodinger

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1923 L. de Broglie:

particle-wave duality

= h/mv


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Broglie argume!t:

ordi!g to #la!c$ a!d %i!tei! &photoelectric e'ect()

rgy o* a light +ua!ta i:h

*rom pecial relativity &%i!tei!()&m,2cp2c2(1/2

or light) the ret ma m,=,) % = pc.

here*ore h= pc

i!ce

= c

hu p = h/ or h/p*or light


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de Broglie co!ecture: &1923(

4 i* light +ua!ta i a real particle) a uggeted i!

photoelectric e'ect) a!d the 5ompto! e6perime!t) therelatio!hip 7etwee! the particle mome!tuma!d it wavele!gth &patial periodicity( ca!!ot 7e u!i+ue tout light) perhap maive particle li$e electro! may alohave ome i!ter!al periodicity. 48

&By the!) Bohr had already co!ectured periodicity motio! o*electro! i! atomic or7it i! the Bohr model.(

! all wave) the phae velocity =. * electro! are wave)they mut alo have

= %/p &recall %=pc) c=%/p( = h/p) here i the matter wave *re+ue!cy &whatever iti(

;r p = h/&/( = h/&/( = h/

i.e.

= h/p) i!ce p=mv *or maive particle)


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or thi matter wave to ma$e e!e) it group velocityha to 7e the particle velocity v)

i it!ed a

vg= d/d$) =2) $ =2/

or light) vg= d/d$ = d%/dp = d&pc(/dp = c &phae

velocity(

or matter wave)

vg= d%/dp =d&&m,2cp2c2(1/2(/dp = v

?owever) the phae velocity o* matter wave=%/p=mc2/mv=c2/v @ c.


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&de Broglie) 192A(


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Davio!-ermer e6perime!t


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ragg co!ditio!: = 2di!


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"*ter Davio!-ermere6perime!t) the wave!ature o* maiveparticle wa !o lo!geri! dou7t.

eutro! optic 7ecamea power*ul tech!ology.


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NIST Center for Neutron Research

= h/mv C 1/01/2

cold !eutro! havelo!g wavele!gth

Bragg co!ditio!:! = 2di!


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1999-2,,,


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eutro!Di'ractio!


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ummarie the crucial co!ceptual tep:


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In 1926, Prof. P. Debye (ETH) sai a! a se"inar #i$en by %&'roin#er one ro#ie*s +a+er,if e ro#ie*s -a$e +i&!re is !o be of sbs!an&e, !'ere "s! be a -a$ee/a!ion . Er-in, -'y on*! yo !ry n i! an re+or! !o s ne! -ee

%&'roin#er i 'is 'o"e-or, an #o! a obe Prie a!er for i!.


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1913 Bohr model:tatio!ary or7it

1EEF

Balmer erie

t e6plai! Balmererie) 7ut it iagai!t the law o*%GH:circular motio!re+uire radialacceleratio!)acceleratio! o*

charged particle willemit radiatio!)tatio!ary or7it ca!lat le tha! 1 !

accordi!g to %GH.


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ra!c$ a!d . ?ert: ra!c$-?ert e6perime!t

191


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lecture 2 de broglie and schrodinger

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