1
vote
2answers
64 views

Eigenvalues being physical observables

I think I'm comfortable with the PDE solutions to the Schrodinger equation. But as soon as we start putting these values in a matrix (in dirac notation), I lose my understanding and everything ...
1
vote
2answers
47 views

How does Dirac conclude that $X_r(c_r)$ cannot vanish?

On page 32 of Dirac's book Principles of Quantum Mechanics, he considers the case when the linear, Hermitian$^1$ operator $\xi$ satisfies an algebraic equation $$\phi(\xi)\equiv(\xi - c_1)(\xi - ...
6
votes
1answer
139 views

Eigenstate of field operator in QFT

Why don't people discuss the eigenstate of the field operator? For example, the real scalar field the field operator is Hermitian, so its eigenstate is an observable quantity.
2
votes
1answer
493 views

Why are orthogonal functions and eigenvalues/functions so important in quantum mechanics?

The mathematics and physics we have studied so far at university are heavily focused around the idea of orthogonal functions, orthogonality, sets of solutions, eigenvalues and eigenfunctions. Why ...
1
vote
1answer
101 views

Weird Behaviour of the act of measurement to a quantum system

I and my friend were disputing about some weird behaviour of the act of measuring some observables quantities e.g. Energy, position. But I still don't think what he said is strictly true. He said" ...
0
votes
2answers
2k views

Expectation Values in Quantum Mechanics

Why is the expectation value what it is? Why don't you apply the operator, then multiply that by it's conjugate?
-1
votes
1answer
163 views

Wavefunction operators and the observable [closed]

So I got this from the exam I had yesterday. I couldn't really answer it other and it played on my mind through the night Show that if a wave function $\psi$ , is an eigenfunction of an operator [Q], ...
6
votes
2answers
608 views

Eigenvalues of a quantum field?

Fields in classical mechanics are observables. For example, I can measure the value of the electric field at some (x,t). In quantum field theory, the classical field is promoted to an operator-valued ...