mirror of
https://asciireactor.com/otho/phy-4600.git
synced 2024-12-04 18:45:06 +00:00
15 lines
722 B
Plaintext
15 lines
722 B
Plaintext
|
(1) A general state vector is represented by |Ψ> (a ket)
|
||
|
|
|
||
|
|
(2) A physical observable is represented by an operator A that acts on |Ψ>
|
||
|
|
|
||
|
|
(3) The possible measurements of an observable are the eigenvalues aₙ of the operator A
|
||
|
|
|
||
|
|
(4) The probability of measuring eigenvalue aₙ is given by Paₙ=|<aₙ|Ψ>|²
|
||
|
|
|
||
|
|
(5) After a measurement A that yields aₙ, the quantum system is in a new state that is the normalized projection of the original system ket onto the ket (or kets) corresponding to the result of the measurement:
|
||
|
|
|Ψ'> = Pn|Ψ> / √(<Ψ|Pn|Ψ>)
|
||
|
|
|
||
|
|
(6) The time-evolution of the quantum system is determined by the Hamiltonian operator H(t) through the Schrodinger equation
|
||
|
|
ιħ(d/dt)|Ψ(t)> = H(t)|Ψ(t)>
|
||
|
|
|