Physics 2 - Lecture 7: Quantum Mechanics - Huynh Quang Linh

Nội dung text: Physics 2 - Lecture 7: Quantum Mechanics - Huynh Quang Linh

1. QUANTUM MECHANICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
2. CONTENTS • Wave – Particle Duality of Matter • De Broglie’s Hypothesis – Matter wave • Diffraction of electron wave by single slit • Heisenberg’s Uncertainty Principle
3. “Double-slit” Experiment for Electrons  Electrons are accelerated to 50 keV l = 0.0055 nm  Central wire is positively charged bends electron paths so they overlap  A position-sensitive detector records where they appear.  << 1 electron in system at any time [A. TONOMURA (Hitachi) pioneered electron holography] Exposure time: 1 s 10 s 5 min 20 min
4.  M (x,y,z) r Electromagnetic Wave: z k z Consider a light plane wave, O v propagating in the z direction: Wave function at point O: o = A cos (t) Wave function at point M: (M, t)=A cos ((t-z/v)) =Acos(t-kz) (M,t) Acos(t k.r) in complex description : Ψ(M,t) Ae-i(t-k.r)  wavenumber : : complex wavefunction i(t-k.r)   2 2 Ψ(M,t) Ae  k with theconvention : Ψ(M,t) Re Ψ(M,t) v vT l    2 real realpart of complex wave wavevector :k n wave function function l n : unit vector
5. Wave function of a monochromatic wave Wave function of a electromagnetic monochromatic wave i(t k.r) (M,t) oe Wave function of a free particle of momentum p and kinetic energy E: i (Et p.r) i(t k.r)  (M,t) oe oe
6. DIFFRACTION OF ELECTRONS BY 2 SLITS
7. The statistic meaning of the Wave Function of a particle: Intensity of Light is proportional to the square of the amplitude of the wave at that point: I=kA2 (W/m2) Intensity of Light is proportional to the photon density at that point. I=e.c =N. hf.c 2 1 2 1 B e: energy density of electromagnetic wave. (J/m3) e oE 2 2  N : photon density (photon/m3) o IA2 N The amplitude squared of the wave is proportional to the photon density => proportional to probability of finding the photon per unit volume. For the matter wave , the amplitude squared of the wave is the probability of finding the particle per unit volume= probabilty density 2 * 2 | (r,t) | (. ) o
8. Constraints on Wavefunction In order to represent a physically observable system, the wavefunction must satisfy certain constraints: (x,t) - Must be a single-valued function - Must be normalizable. This implies that the wavefunction approaches zero as x approaches infinity. - Must be a continuous function of x. - the first derivative of (x,t) must be continuous
9. HEISENBERG’S UNCERTAINTY PRINCIPLE OF POSITION AND MOMENTUM The uncertainty in the x position x. p h x a a x x a Consider the diffraction of electrons by 2 2 a single slit. The uncertainty in the x-component of the momentum : x 0 px psin q px psin q l è sin q a q x a h l h p p psin q . x x l a a h x. p a. x a x. px h
10. x 5 10 11m   x. p p x 2 x 2 x  p 1.055 10 24(kg.m / s) x min 2 x  p 1.055 10 24(kg.m / s) x min 2 x p 1.055 10 24(kg.m / s) p2 (1.055 10 24)2 KE 6.1 10 19 J 3.82eV 31 2me 2 9.1 10