Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

Homework Phys 452 Tuesday Mar 13: assignment # , 9.18, 9.19 Friday Mar 16: assignment # , 9.9, 9.10, 9.12, 9.14

Quiz 23a Phys 452 What is true about time-dependent perturbation theory? A.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 E.We use the perturbation to find out the probability of measuring the particle in a given state as a function of time

Two- level systems Time- dependent perturbation Phys 452 In case of off-diagonal perturbation

Two- level systems Time- dependent perturbation Phys 452 Zero order: First order: Second order:

Two- level systems Time- dependent perturbation Phys 452 Initial conditions Application: sinusoidal perturbation First order Probability of transition:

Two- level systems Time- dependent perturbation Phys 452 Sinusoidal perturbation Probability of transition: t P(t) for a given frequency 

Two- level systems Time- dependent perturbation Phys 452 Sinusoidal perturbation Probability of transition:  P(  ) for a given time t Resonance effect

Two- level systems Time- dependent perturbation Phys 452 Pb 9.7 Probability of transition:  P(  ) Rabi flopping frequency

Constant perturbation for a lap of time Phys 452 Pb 9.18“Brick” in the infinite square well, from t=0 to T 0 a n=1 n=2 V0V0 Express the perturbation integrate the equation: Get the probability of transition at time T:

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

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

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

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

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

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

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

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

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

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

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

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