709292
Descrição
Mapa Mental por franz.sciortino, atualizado more than 1 year ago
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Criado por franz.sciortino
mais de 10 anos atrás
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Quantum Mechanics
- Finite Square Well,
potential step and barrier
- Simple Harmonic
Oscillator (SHM)
- Five postulates of QM
- post.2 --> Properties of Hermitian operators
- post.1 --> wavefunctions of
dynamical variables
- post.3 --> x and p operators, others for
dynamical variables (as classically)
- post.4 --> prob. densities by sum of
expansion coefficients (squared)
- post. 5 --> time dependence as by TDSE
- Wavefunction collapses by interferences with the system
- Wavefunction collapses by interferences with the system
- post.2 --> Properties of Hermitian operators
- Commutators (Herm.) vs. anticommutators (anti-Herm.)
- Compatibility of observables --> common set
of eigenstates (e.g. H and p for free particle)
- If Q & R commute and have unique
eigenvalues, then are compatible
- If Q & R commute and have unique
eigenvalues, then are compatible
- Compatibility of observables --> common set
of eigenstates (e.g. H and p for free particle)
- Dirac notation: see summary table in lect.10 notes
- Expectation values and uncertaity
- <Q>=sum((a_n)^2 *q_n) or
<Q>= int(psi* Q psi)
- Ehrenfest Theorem: eq. of motion for expectation
values of observables follow classical counterparts
- RMS spread: Delta(q)= int(mod(Q psi)^2)
or <Q^2>-<Q>^2
- HUP: apply Schwartz inequality to difference operators
(e.g. Q') with commutators and anticommutators;
- Find that <[Q', R']> = <[Q,R]>
- Consider only imaginary part, with
[x,p] included, for the HUP statement
- Consider only imaginary part, with
[x,p] included, for the HUP statement
- Find that <[Q', R']> = <[Q,R]>
- <Q>=sum((a_n)^2 *q_n) or
<Q>= int(psi* Q psi)
- Continuous eigenvalues: swap Kronecker with Dirac
delta + integration rather than summation (see notes
lect.14)
- Continuous eigenstates cannot be normalised - mostly
multiply by a Gaussian factor to get wavepackets
- Continuous eigenstates cannot be normalised - mostly
multiply by a Gaussian factor to get wavepackets
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