Transcript Document

PHYS 30101 Quantum Mechanics
Lecture 9
Dr Jon Billowes
Nuclear Physics Group (Schuster Building, room 4.10)
[email protected]
These slides at: www.man.ac.uk/dalton/phys30101
Plan of action
1. Basics of QM
Will be covered in the following order:
2. 1D QM
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
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
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:
Quantum Beats
Harmonic oscillator
wavefunctions
Quantum beat between n=0 and
n=1 eigenstates