lecture_10_07b

lecture_10_07b - 05/12/09 Physics 13 - Fall 07 - G.R....

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 1 EM wave-particle duality • Maxwell: E nergy/vol ~ E 2 (or E 2 + B 2 ) • But quanta have E = h ν . How to reconcile? • Note that 100 W light bulb → 30 W visible light with peak λ near 500 nm, • so ν =c/ λ =6x10 14 s-1 • and each γ has E=6.6x10-34 J•s • 6x10 14 s-1 • ~4x10-19 J. • Hence no. γ ’s ~ 30J/s÷ 4x10-19 J • ~ 8x10 19 γ ’s/sec E x c 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 2 EM wave interference • E = E 1 + E 2 and | E | 2 ≠ | E 1 | 2 + | E 2 | 2 • As | E | 2 (~ Probability for γ ’s) decreases to few γ ’s get same pattern on the average monochromatic-no γ ’s, E 2 =0- γ ’s, E 2 >0 red=dark, white=bright 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 3 Light, bb’s, electrons • Compare EM interference with bb’s shot through 2 slits ( ℘ robability = ℘ 1 + ℘ 2 ) • Electrons are like light, not bb’s. 2200 Ψ = Ψ 1 + Ψ 2 and ℘∝ | Ψ | 2 =| Ψ 1 + Ψ 2 | 2 ≠ | Ψ 1 | 2 + | Ψ 2 | 2 2200 Ψ (x ,t) is the amplitude for an electron at x ,t. • | Ψ (x ,t)| 2 is Probability Distribution Function or Probability Density, with | Ψ (x ,t)| 2 ∆ V the - 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 4 Normalizing probability • Necessary mathematical requirement for physical sense 2200 ℘ (x ,t)=| Ψ (x ,t)| 2 in 3-dim space • In 1-dim ℘ (x,t)=| Ψ (x,t)| 2 and ℘ (x,t)dx is probability in length dx • So need ∫ All x dx ℘ (x,t) =1 since single electron is somewhere • This is normalization of probability and amplitude Ψ 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 5 Travelling waves • Time development of Ψ is the dynamics in QM • Travelling plane wave (1-dim) is a solution for a free particle : x V Real( Ψ ) λ 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 6 Plane wave variables Ψ ( x , t ) = A sin( kx- wt ) where k = 2 p l and w = 2 pn for a travelling plane wave. But for Quantum Physics l = h p so h k = p . Also p 2 2 m = E h w = h 2 k 2 2 m dispersion velocity V = l n = w k depends on k (= 1 2 p m ) - h 2 2m 2 x 2 Y ( x , t ) + U ( x )Y ( x , t ) = ih t Y ( x , t ) U(x)=0 for free particles 05/12/09 Physics 13 - Fall 07 - G.R. Goldstein 7 Interpretation of plane wave • Infinite in extent ⇒ completely unlocalized particle with definite wavelength & frequency (for precise spatial shape & time...
View Full Document

This note was uploaded on 03/27/2008 for the course PHY 13 taught by Professor Garyr.goldstein during the Fall '04 term at Tufts.

Page1 / 30

lecture_10_07b - 05/12/09 Physics 13 - Fall 07 - G.R....

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online