Hermitian Operator: Definition & Overview

sm09
Messages
9
Reaction score
0
what is it?
 
Physics news on Phys.org
an operator that is hermitian!

in a matrix representation, it means that the diagonal Mii is real, and any Mij is the complex conjugate of Mji. this gives the hermitian conjugate of M (transpose and conjugate) is itself.or... google Hermitian

it represents a measurable quantity in QM.

ps.
am i right?
 
Last edited:
This question is well enough described in a any QM textbook. You do not make much effort to look there. In simple, Hermitian operator is the observable represetation, or if not rigorously speaking, it reflects the measurement procedure in a some quantum state. For example, let we have an spin-up directed electron state \left | + \right>. Measurement of the z-directed spin by \hat S_z in this state is reflected in the equality \hat S_z \left | + \right> = +\hbar/2 \left | + \right>. This mean the result you will get is +\hbar/2. A key feature of a Hermitian operator is real numbers of their eigenvalues.
 
Last edited:

Thread 'Schrödinger equation and classical wave equation'

Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
View full post »

Thread 'Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
View full post »

Thread 'Is Maxwell's electromagnetism an effective (field) theory?'

Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...
View full post »

Similar threads

I A strange definition for Hermitian operator
Replies
3
Views
1K
B Is the Momentum Operator Hermitian? A Proof
Replies
7
Views
2K
I Action of an Hermitian unitary operator member of SU(2)
Replies
15
Views
383
I How to derive momentum operator in position basis via its definition?
Replies
6
Views
1K
I Motivation behind the Operator-Formalism in QM
Replies
3
Views
1K
I Completeness of Eigenfunctions of Hermitian Operators
Replies
22
Views
2K
I Eigenstates of particle with 1/2 spin (qbit)
Replies
24
Views
2K
I Proof of Commutative Operators for Simultaneous Measurement
Replies
14
Views
2K
I Dirac Notation for Operators: Ambiguity in Expectation Values?
Replies
5
Views
1K
A Converting between field operators and harmonic oscillators
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top