# 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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### 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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### Superposition and simultaneous observation

Trying to understand superposition. Ok, so double slit experiment. The multiple paths the particle simultaneously travels interfere with each other but as it is absorbed, it chooses one "actual" ...
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### Is the probability current an observable?

Is the probability current in Quantum Mechanics an observable? If so, how can it me measured (directly or indirectly)?
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### “Independent simultaneous eigenbras” in Dirac's book 'Principles of Quantum Mechanics'

I've been puzzling through this book off and on and can usually work out what is going on via other external references on the Intertubes. But, this paragraph from pages 55 and 56 has me a bit ...
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### Compatible Observables and Measurement

Suppose $A$ and $B$ are compatible observables (i.e. $[A,B] = 0$). We take the eigenkets of $A$ to be $|a_1 \rangle \ldots |a_N \rangle$. Further, we suppose that the first $k$ eignekets of $A$ are ...
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### Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
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### Relativistic Commutation relation for momentum and position

We all know that the canonical commutation relation give you $$[x_i,p_j]=i\hbar\delta_ij,$$ is there a relativistic version such as $$[x^a,p_b]=i\hbar\delta_a^b?$$ If so what is the time ...
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### Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the SchrÃ¶dinger we can find the probability of finding the particle at some points in the box. How can we find the probability of ...
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### Motivating Irreducibility of Hilbert Space for Quantization Axioms

In the context of geometric quantization, we usually look for a map from the Poisson algebra of classical observables to the algebra of quantum observables (or rather, a sub-algebra of the classical ...
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### Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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### What are physical observables that are connected to orbital angular momentum?

We considered a system that is confined to a curved surface. In the quantization process, we have obtained an additional orbital angular momentum that are from the surface geometrical deformation. Now ...
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### Is there a physical significance to non-normal states of the algebra of observables?

Quantum theory may be formalized in several different ways. Generally, the physical discussion of different states of a quantum system distinguishes pure and mixed states, and then subsumes both in a ...
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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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### 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. ...
A physical quantity can be represented by the following form: $A = a_1\sigma_1 + a_2\sigma_2 + a_3\sigma_3$ where $\sigma$ matrices are Pauli matrices. Also suppose that there is \$B = b_1\Sigma_1 + ...