class36 - What brought us to the Schrd. equ? Today: Review...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Today: Review Exam: Tomorrow 7:30 - 9:15pm, MEUN E-050 Topics: All we have done so far (TZD: 1-7) Allowed materials: Two letter paper-sized, hand- written cheat-sheets (all four sides) and a Calculator. But: Textbooks, cell phones, laptops, radios, TVs, pot-plants, aquarium, smokes, beer, etc. are not allowed. What brought us to the Schröd. equ? EM-waves Wave equation: Probability to find photon: E(x,t) EM wave function: |E| 2 dx De Broglie: ‘Nature is symmetric’ ‘Matter is a wave’ λ =h/p 2 2 2 2 2 1 t E c x E = (1D In free space) E = hf Energy x V(x) n=1 n=2 n=3 ψ (x) t t x i t x t x V x t x m Ψ = Ψ + Ψ ) , ( ) , ( ) , ( ) , ( 2 2 2 2 h h Wave equation: Probability to find particle: Wave function: t t x const x t x Ψ = Ψ ) , ( . ) , ( 2 2 1D In free space: Matter waves: Ψ(x,t) |Ψ| 2 dx Vibrations on a string: Electromagnetic waves: Classical wave Equations 2 2 1 y y 2 2 1 E E x y E x 2 2 2 t v x = v = speed of wave 2 2 2 t c x = c = speed of light Magnitude is non-spatial: = Strength of Electric field Magnitude is spatial: = Vertical displacement of String Solutions: E(x,t) Solutions: y(x,t) EM waves vs. matter waves EM Waves (light/photons): Amplitude E = electric field E 2 tells us probability of finding photon. Maxwell’s Equations: Matter Waves (electrons, etc.): Amplitude ψ = “wave function” | Ψ | 2 tells us probability of finding particle. Schrödinger Equation:
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

class36 - What brought us to the Schrd. equ? Today: Review...

This preview shows document pages 1 - 2. Sign up to view the full document.

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