Lecture Physics A2: Fundamental of Quantum Mechanics - PhD. Pham Tan Thi

Lecture Physics A2: Fundamental of Quantum Mechanics - PhD. Pham Tan Thi present the content diffraction of light/electron by one slit, double-slits experiments for electrons, wave-particle duality, De Broglie’s hypothesis, for a non-relativistic free particle,...
Nội dung trích xuất từ tài liệu:
Lecture Physics A2: Fundamental of Quantum Mechanics - PhD. Pham Tan ThiFundamental of Quantum Mechanics Pham Tan Thi, Ph.D. Department of Biomedical Engineering Faculty of Applied Sciences Ho Chi Minh University of TechnologyQuantum MechanicsDiffraction of Light/Electron by One SlitDouble-slits Experiments for Electrons (Wave-like character of electrons) Wave-Particle Duality Energy in Energy out A beam of light can be thought as .... ... a flux of particle ... an electromagnetic wave (Newton/Planck/Einstein) (Huygens/Maxwell/Hertz) Electric Field Wavelength λZero mass, speed: c = 3 x 108 m/s Direction of propagationEnergy carried by each particle: h = 6.6262 x 10-34 J.s (Planck) c = λν Dispersion relation ν (frequency) = 1/T (period) (Free space) Particle (Photon): Wave (Electromagnetism): - Photoelectric Effect - Interference - Compton Effect - Diffraction de Broglie’s Hypothesis “Light can behave like a particle and Matter/Electron can behaves like a wave Energy of Photon by Special Relativity: E = pc Energy of Photon by Planck’s theory: E = h⌫ de Broglie’s wavelength: h = p Wave if λ > ScaleIt turns out that everything’s kind of mixed together at the fundamentalmicroscopic scale. For a Non-relativistic Free ParticleMomentum is p = mv, here is v is the speed of the particle Total energy of a free particle, E, is kinetic energy: h h h B = = =p p mv 2mE p2 mv 2 E=K= = 2m 2 Bullet: m = 0.1 kg; v = 1000 m/s 36 ➔ B ⇡ 6.63 ⇥ 10 mWhat is the de Broglie’s Wavelength of an Electron?What is the de Broglie’s wavelength of an electron moving at 2.2 x 106 m/sWhat is the de Broglie’s Wavelength of an Electron?What is the de Broglie’s wavelength of an electron moving at 2.2 x 106 m/sNow this is really really fast: 2.2 million meters per second. But it’s notrelativistic. It’s is still slow compared to the speed of light so we can stilldo everything fairly classically. 31 p = mv = 9.1 ⇥ 10 ⇥ 2.2 ⇥ 106 [kg m/s] = 2 ⇥ 10 24 N.s 34 24 10 = h/p = 6.626 ⇥ 10 /2 ⇥ 10 = 3.33 ⇥ 10 mThis is important number. This speed is a kind of average speed of anelectron in ground state of hydrogen. Accelerated What is the de Charges Broglie’s (electrons, Wavelength protons) of a Person? Producede Broglie’s theory can be extended to show that all matter exhibits thesame wave-particle duality as light. This means everything in the universecan act like a wave: h = and h = 6.626 x 10-34 m2kg s-1 mvThis shows that an object’s wavelength gets smaller when the moremassive it is, and the faster it is moving.If a person has a mass of 75 kg, and is jogging at 8 km/h (which is about2.2 m/s), then Accelerated What is the de Charges Broglie’s (electrons, Wavelength protons) of a Person? Producede Broglie’s theory can be extended to show that all matter exhibits thesame wave-particle duality as light. This means everything in the universecan act like a wave: h = and h = 6.626 x 10-34 m2kg s-1 mvThis shows that an object’s wavelength gets smaller when the moremassive it is, ...