What is observables: Definition and 115 Discussions

In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value.
Physically meaningful observables must also satisfy transformation laws that relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations that preserve certain mathematical properties of the space in question.

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  1. S

    Does Commuting with Hamiltonian Ensure Observables' Commutator is Constant?

    [SOLVED] commutation of observables Homework Statement Prove: If the observables (operators) Q1 and Q2 are both constant of the motion for some Hamiltonian H, then the commutator [Q1, Q2] is also a constant of the motion. okay, first question.. am i being asked to prove that [[Q1, Q2], H] =...
  2. B

    Understanding observables in QM

    Hi community, In the past weeks I'm busy ordering my thought on quantum mechanics. Somehow I really like to understand this part of physics, I don't want to just make a good exam. That's why I started writing down everything I know on quantum mechanics (from a mathematical point of view) and...
  3. C

    Can measuring certain operators in a quantum system have deadly consequences?

    A variant of Schrödinger's cat experiment: Consider operators with eigenstates of the form |dead> + |alive>. If we could somehow measure such an operator we could kill a healthy person by just observing. :smile: So, what is going on here? Consider a simpler problem: A particle in...
  4. I

    QM - Can We Conclude [A,B]=0 with {|a',b'>}?

    Homework Statement If A and B were observables, and say the simultaneous eigenkets of A and B {|a',b'>} form a complete orthonormal set of base ket. Can we conclude that [A,B]=0? 2. The attempt at a solution Assume {|a',b'>} is incompatible: AB|a',b'>=a'b'|a',b'> <-- skipped several steps...
  5. P

    Duality between generators of changes and observables in QM

    I've posted similar questions on a different forum previously, but since I'm feeling a bit guilty about going on at the one person there who answers, I'll post these here. Hope it's ok if I don't follow the template since they're more conceptual than a standard problem. Any help appreciated...
  6. T

    Are 'Observables' Considered a Valid Term in Quantum Mechanics?

    Is ``OBSERVABLES'' a word? I know ``OBSERVABLE'' (singular is), but what about the plural?
  7. W

    Question on observables of QFT

    Hi, In Weinberg's QFT book(section 2.2), he said after proved the generator of the symmetry group is Hermitian and can be a candidate for an observable: My questions: 1. Does the observable here mean at least in principle, we can measure it in experment? 2. Does generator of any symmetry...
  8. A

    Observables of position and momentum have a continuous spectrum

    could someone explain this paragraph taken from "concepts of modern physics" by arthur beiser pg175? I'm having trouble understanding it... "A dynamical variable G may not be quantized. In this case, measurements of G made on a number of identical systems will not yield a unique result but...
  9. F

    Understanding the Set of Commuting Observables

    Hi, I've had a question ever since my quantum classes that's pretty simple I guess, but still seems to elude me. So here it is: One text I used for quantum (Liboff's "Introductory Quantum Mechanics") says that in classical mechanics, there is a "vector of the state" of a system, that...
  10. M

    Observables in Quanum Mechanics

    In the context of observables in QM the rate of change of the In the contest of observables in QM the rate of change of the expectation value of an observable A is defined by: d<A>/dt= d< Y | A Y>/dt = < d Y/dt | A Y > + < Y | dA/dt . Y > + < Y | A dY/dt> My question is about the second...
  11. F

    Understanding Operators & Observables: Averages & Variance

    I have trouble understanding operators and observables: Does <A> the average value of an observable and the variance depend on the state of the system? What does it have to do with the Hamiltonian? Thanks!
  12. Z

    Observables as a function of energy

    The question is: Prove that, for a 1-D harmonic oscillator, every conserved observable is a function of the energy. Find, for the 3-D harmonic oscillator, some conserved observable not a function of the energy and angular momentum. My first problem with this question is I'm not sure what...
  13. humanino

    Self-adjoint/hermitean operator vs observables

    An observable in QM is to be represented by a self-adjoint/hermitean operator, so that the eigenvalues are real numbers. I could not find the answer to : are all self-adjoint/hermitean operators actually observables ? Thank you for any help !
  14. kakarukeys

    Do Incompatible Observables Have Common Eigenfunctions?

    Incompatible observables do not share a complete set of common eigenfunctions, because their operators do not commute. It seems that, incompatible observables like x and p_x, S_x and S_y do not have any common eigenfunction at all. Can anyone give a concrete example of a pair of...
  15. A

    Meaning of operators for observables.

    I understand that observables in quantum mechanics are represented by hermitian operators, which are converted into a matrix when expressed in a particular basis. I also understand that when the basis used is an eigenbasis of the operator, the matrix becomes diagonal, having the eigenvalues as...
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