Tagged Questions

A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical ...

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How to determine the observables rigorously?

In Quantum Mechanics, as I know, if a system is described by a Hilbert space $\mathcal{H}$, each physical quantity is associated with some hermitian operator $A : U\subset \mathcal{H}\to \mathcal{H}$ ...
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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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Is the perturbation Hamiltonian an observable?

In fine structure calculation we use the perturbation theory. The basic Hamiltonian $H_0$ is perturbed as: $H = H_0 + W$ First, the basic problem assume that $H_0$ is an observable. That allows to ...
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spin independent observable [closed]

Let's consider a spin independent observable $O$ (the terms of the operator don't depend upon the spin operator). If we are interested to find an eigenfunctions' basis of the wave-functions' space, ...
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Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
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How much information does the Hamiltonian contain in quantum mechanics? [closed]

Given a Hamiltonian, let's say of a many-body system, through the Schrodinger equation,in principle we can find the eigenfunctions and their corresponding eigenvalues (spectrum). Now given an ...
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Expectation value of operators in quantum mechanics

Can the expectation value of an operator be zero?
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The delta function as an eigenfunction of the position operator explanation

$\delta (\textbf{r})$ can be interpreted as a wavefunction. [...] It is non-vanishing only for $\textbf{r}=0$. [...] $\delta(\textbf{r})$ is an eigenfunction of the position operator with eigenvalue ...
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Eigenstate vs collapsed wave function

An eigenstate, or determinate state, is a state where the measurement of some observable always yields the same result. This means that the standard deviation of the observable is zero. If a ...
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Why tensor product? [duplicate]

Let $A$ an $B$ be two discrete observables (like spins). When exactly and why we have to consider their tensor product when talking about the mutual observation of the corresponding phenomena?
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What is the correct way to treat operators that has “time” in QM? [duplicate]

I don't know if this question has already been resolved but considering that $i\hbar\partial_t$ is the energy operator, and $\partial^2_t$ is the waves operator (or helmholtz), I can't accept that $t$ ...
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Eigenstates into which a system can be projected after a measurement

I'm currently reading Dirac's Principles of Quantum Mechanics, on page 36, he says: Another assumption we make connected to the physical interpretation of the theory is that, if a certain real ...
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If I want to determine a particle's momentum or position, do I get this information from the wave function?

I am confused about how one measures the dynamical variables (eg position) of a particle. I thought the wave function $\Psi(x,t)$ was the probability amplitude and $|\Psi(x,t)|^2$ represents the ...
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What are the methods of experimentally measuring the observables in quantum mechanics?

Perhaps due to the limited number of textbooks on quantum mechanics I have consulted, I have seen presented the fundamental principles related to observables, but have never seen a somewhat systematic ...
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A new operator which gives direction of the momentum of the particle in 1-d space, preserving everything else : Need practical applications

I have introduced a new observable (unitary self-adjoint operator) which seems to give the direction of the momentum of the particle in 1-dimensional space, without disturbing anything else. We can ...
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Is there a deterministic observable that has only single eigenvalue?

Is there an observable in quantum mechanics which has only one eigenvalue and an eigenspace associated with that single eigenvalue? This observable is deterministic in the sense that it gives same ...
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Importance of anti-self adjoint operators in quantum mechanics

I learnt that the observables are self-adjoint operators working on wave functions which live in a Hilbert space. The eigenvalues of these operators are real and appear as outcome of measurements. ...
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Is there a connection between Lie Groups and observable quantities in physics?

Good evening everybody. I have some questions about the relation between Lie groups and observables in physics. Indeed, taking the example of spin formalism of Quantum mechanics I know that Pauli's ...
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What are observables? [closed]

What are observables and how are they related to quantum decoherence and wavefunction collapse. I read this: Observables - what are they? but it was about the technical details on observables. Even ...
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What does observation mean in two-slit electron diffraction experiment? [duplicate]

My question is clear, that I ask: What do we mean by "observation" in 2-slit experiment for electrons (or any other wave-particle)? You know, we say that :"if we observe the electron, it shows a ...
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Why is quantum mechancis is not content with symmetric operators, but wants self-adjoint operators?

A symmetric operator has only real eigenvalues and different eigenvectors corresponding to different eigenvalues are orthogonal. These are exactly what we want for a physical observable. I think ...
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Physical observables and hermiticity

Is it necessary for an operator to be Hermitian in order to be a physical observable or is it just sufficient that the operator obeys the eigenvalue equation? If I were to check whether an operator is ...
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Why do we care about compatible observables?

Going through my first treatment of quantum mechanics at the Griffiths level, and I was wondering why we care about observables being compatible and what is the significance of having an eigenstate ...