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Physics 452

Physics 452. Quantum mechanics II Winter 2012. Karine Chesnel. Phys 452. Homework. Tuesday Mar 13 : assignment # 15 9.7, 9.18, 9.19 Friday Mar 16 : assignment # 16 9.8, 9.9, 9.10, 9.12, 9.14. Phys 452. Quiz 23a. What is true about time-dependent perturbation theory?.

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Physics 452

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  1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

  2. Phys 452 Homework Tuesday Mar 13: assignment # 15 9.7, 9.18, 9.19 Friday Mar 16: assignment # 16 9.8, 9.9, 9.10, 9.12, 9.14

  3. Phys 452 Quiz 23a What is true about time-dependent perturbation theory? • The perturbation basically induces a modification • of the phase of the wave function • B. This theory applies exclusively for time-dependent potential • C. The perturbation has to occur for a very short time • D. The perturbation is inducing a change in the transition energy • between atomic levels as a function of time • We use the perturbation to find out the probability of measuring • the particle in a given state as a function of time

  4. Phys 452 Two- level systemsTime- dependent perturbation In case of off-diagonal perturbation

  5. Phys 452 Two- level systemsTime- dependent perturbation Zero order: First order: Second order:

  6. Phys 452 Two- level systemsTime- dependent perturbation Application: sinusoidal perturbation Initial conditions First order Probability of transition:

  7. Phys 452 Two- level systemsTime- dependent perturbation P(t) for a given frequency w t Sinusoidal perturbation Probability of transition:

  8. Phys 452 Two- level systemsTime- dependent perturbation P(w) for a given time t Resonance effect w Sinusoidal perturbation Probability of transition:

  9. Phys 452 Two- level systemsTime- dependent perturbation Probability of transition: Rabi flopping frequency P(w) w Pb 9.7

  10. Phys 452 Constant perturbation for a lap of time • Express the perturbation n=2 • integrate the equation: n=1 a 0 V0 • Get the probability of transition at time T: Pb 9.18 “Brick” in the infinite square well, from t=0 to T

  11. Phys 452 Emission and absorption of a radiation Possibilities of • Absorption • Emission Interaction between the atom and electromagnetic wave

  12. Phys 452 Quiz 23b In a system at equilibrium, Absorption and Emission can not occur simultaneously A. True B. False

  13. Phys 452 Emission and absorption of a radiation Assuming the wavelength of the light is large In comparison to the atom with Expression for the perturbation z x y

  14. Phys 452 Emission and absorption of a radiation Sinusoidal perturbation Probability of absorption

  15. Phys 452 Emission and absorption of a radiation Initial conditions (same equation, except ) Probability of emission

  16. Phys 452 Emission and absorption of a radiation Natural de-excitationlifetime of excited state Chain reaction in the emission: amplification (when inversion of population) Spontaneous emission No incident light to trigger the de-excitation Natural de-excitation: explained by the presence of zero-point radiation(quantum electrodynamics) Application: LASER Pb 9.19Spontaneous absorption?

  17. Phys 452 Stimulated emission and absorption: Transition rate • Take into account the non-monochromaticity of the light

  18. Phys 452 Stimulated emission and absorption: Transition rate z p we need x y with • Account for the isotropy of emission/absorption process in 3D

  19. Phys 452 Emission and absorption: Einstein coefficients : stimulated absorption : stimulated emission : spontaneous emission rate Thermal equilibrium Boltzman distribution of particles Analogy with Planck’s blackbody formula

  20. Phys 452 Emission and absorption: Einstein coefficients Comparing the two processes Find the critical T at given w or the critical w at given T for which Planck’s blackbody radiation Pb 9.8: competition between stimulated and spontaneous emission...

  21. Phys 452 Emission and absorption: Einstein coefficients The density of zero-point radiation: Occupation number = 1 in blackbody radiation formula (5.111) Retrieve expression for A Pb 9.9: deriving spontaneous emission as a stimulated process

  22. Phys 452 Spontaneous emission: Lifetime of excited state Lifetime of excited state When several decay modes Overpopulated excited state, not at equilibrium

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