1. PHYS 30101 Quantum Mechanics PHYS 30101 Quantum Mechanics Dr Jon Billowes Nuclear Physics Group (Schuster Building, room 4.10) j.billowes@manchester.ac.uk These slides at: www.man.ac.uk/dalton/phys30101 Lecture 9

2. Plan of action 1.Basics of QM 2.1D QM Will be covered in the following order: 1.1 Some light revision and reminders. Infinite well 1.2 TISE applied to finite wells 1.3 TISE applied to barriers – tunnelling phenomena 1.4 Postulates of QM (i) What Ψ represents (ii) Hermitian operators for dynamical variables (iii) Operators for position, momentum, ang. Mom. (iv) Result of measurement 1.5 Commutators, compatibility, uncertainty principle 1.6 Time-dependence of Ψ 1.7 Degeneracy

3. Re-cap Postulate 5: The development of the wavefunction between measurements is governed by the TDSE We consider the case where Ĥ is time-independent, and expand the wavefunction in eigenfunctions of Ĥ All time-dependence is here Eigenfunctions of Ĥ must be time independent We get an expression for the time-dependence of the amplitudes by substitution into the TDSE

4. Postulate 5: The development of the wavefunction between measurements is governed by the TDSE We consider the case where Ĥ is time-independent, and expand the wavefunction in eigenfunctions of Ĥ Substitution in the TDSE gives: General solution to TDSE:

5. Harmonic oscillator wavefunctions Quantum beat between n=0 and n=1 eigenstates Quantum Beats