Lect22_CoherentStates - Summary P2 1 m 2 X 2 2m 2 memorize...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 22: Coherent States PHY851 Quantum Mechanics I Fall, 2008 M.G. Moore Summary What we have learned about the QM SHO: 1 ! = n n n A 1 1 + + = n n n A n = A ( ) n n ! 0 " 0 ( x ) = # $ [ ] % 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 ( + = ! 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 2 X " # i " h P $ % & ( ) ! " # $ % & + = 2 1 A A H h 2 / 1 + = ! n X " 2 / 1 + = ! n P " h ! " m h = memorize
Image of page 1

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 ! 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 just maintain their coherence in the presence of dissipation 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: They are the ‘most classical’ states of the harmonic oscillator They describe the quantum state of a laser Replace the number of ‘quanta’ with the number of
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern