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Quantum Mechanics II: Time-Dependent Perturbation Theory & Two-Level Systems

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This document outlines the assignments and concepts related to Quantum Mechanics II, focusing on time-dependent perturbation theory applied to two-level systems. It includes problems on computing transition probabilities under sinusoidal perturbation, exploring first and second-order perturbations, and comparing results with exact solutions. Key homework assignments involve analyzing various perturbations and initial conditions, which are crucial for understanding quantum transitions. This material is aimed at providing a deeper insight into the principles governing quantum mechanical systems.

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Quantum Mechanics II: Time-Dependent Perturbation Theory & Two-Level Systems

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  1. Physics 452 Quantum mechanics II Winter 2012 Karine Chesnel

  2. Phys 452 Tuesday Mar 13: assignment # 15 Pb 9.7, 9.18, 9.19 Homework Friday Mar 9: assignment # 14 Pb 9.1, 9.2, 9.5, 9.6

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

  4. Phys 452 Two- level systemsTime- dependent perturbation Perturbed state:

  5. Phys 452 Two- level systemsTime- dependent perturbation Initial conditions: Goal: solve for ca and cb First order:

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

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

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

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

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

  11. Phys 452 Time- dependent perturbation Pb 9.1 Electric field perturbation n=2 n=1 Simulation of atomic dipole transition www.falstad.com/qmatomrad/

  12. Phys 452 Time- dependent perturbation Apply this theory for time-independent perturbation Pb 9.2 Second order differential equation Transition between two states still possible

  13. Phys 452 Time- dependent perturbation Apply this theory for time-independent perturbation Pb 9.6 Use the perturbation theory And integrate at second order Compare with the exact answer of problem 9.2

  14. Phys 452 Time- dependent perturbation Two levels system with different initial conditions Pb 9.5 Initial conditions

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