Lect22_CohStates - Lecture 22 Coherent States Phy851 Fall...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 22: Coherent States Phy851 Fall 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Summary Properties of the QM SHO: 1 = n n n A 1 1 + + = n n n A n = A ( ) n n ! 0 ψ 0 ( x ) = π λ [ ] 1/ 2 e x 2 2 2 1 ( x ) = 2 [ ] 1/ 2 2 x e x 2 2 2 n ( x ) = 2 n n ! [ ] 1/ 2 H n x / ( ) e x 2 2 2 n ( x ) = 2 n x n 1 ( x ) n 1 n n 2 ( x ) n n n H ) 2 / 1 ( + = ω h 2 2 2 2 1 2 X m m P H + = + = P i X A h 2 1 ( ) 2 A A X + = ( ) 2 A A i P = h A = 1 X i h P + = 2 1 A A H h 2 / 1 + = Δ n X 2 / 1 + = Δ n P h m h =
Background image of page 2
What are the `most classical states of the SHO? In HW6.4, we saw that for a minimum uncertainty wavepacket with: The uncertainties in position and momentum would remain constant. The interesting thing was that this was true independent of x 0 and p 0, the initial expectation values of X and P . We know that other than the case x 0 =0 and p 0 =0 , the mean position and momentum oscillate like a classical particle This means that for just the right initial width, the wave-packet moves around like a classical particle, but DOESN’T SPREAD at all. 2 osc x λ = Δ osc osc M ω h =
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Coherent States Coherent states, or as they are sometimes called ‘Glauber Coherent States’ are the eigenstates of the annihilation operator – Here α can be any complex number – i.e. there is a different coherent state for every possible choice of – (Roy Glauber, Nobel Prize for Quantum Optics Theory 2005) These states are not really any more ‘coherent’ then other pure states, – they do maintain their coherence in the presence of dissipation somewhat more efficiently In QM the term ‘coherence’ is over-used and often abused, so do not think that it always has a precise meaning Glauber Coherent States are very important:
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 16

Lect22_CohStates - Lecture 22 Coherent States Phy851 Fall...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online