1 / 7

Dirac Notation

Dirac Notation. Each state is denoted by a ket |>. Individual kets are distinguished by the labels placed inside the ket symbol |A>, |B>, etc. States can be added to yield a new state  Superposition To describe STATES, we use vectors. VECTORS represent STATES

ira-washington
Download Presentation

Dirac Notation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dirac Notation Each state is denoted by a ket |>. Individual kets are distinguished by the labels placed inside the ket symbol |A>, |B>, etc States can be added to yield a new state  Superposition To describe STATES, we use vectors. VECTORS represent STATES Each vector can have finite or infinite number of elements A vector has direction and length, and so do the kets A state of a dynamical system = direction of ket Length and sign are irrelevant

  2. kets Complex number If a state is the superposition of 2 states, then the corresponding ket is the linear combination of 2 other kets

  3. Cont. CM: addition of 2 identical statesnew state QM: addition of 2 identical states same state CM: state can have 0 amplitude (no motion) QM: |ket> CANNOT have 0 amplitude, STATE  direction of vector , and if there is a vector, there is a length.

  4. bras To each ket |A>, there corresponds a dual or adjoint quantity called by Dirac a bra; it is not a ket-- rather it exists in a totally different space

  5. Cont.

  6. Length and phase The direction of the vector defines the dynamical state, and the length is not important  We can always use normalized vectors

  7. Operators An operator is a rule that transforms a ket (or bra) in another ket (or bra) Every observable is associated with an operator Notation: I use ^ (as most other authors do), Fayer’s book uses underline

More Related