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3answers
148 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
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1answer
26 views

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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1answer
35 views

“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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1answer
56 views

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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1answer
185 views

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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1answer
115 views

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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1answer
63 views

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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1answer
45 views

Particle in a box - speed probability distribution

Consider a particle in a box with infinite barriers. By solving the Schrödinger 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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0answers
53 views

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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0answers
113 views

On the Equivalence of Schrodinger and Heisenberg Descriptions of Quantum Mechanics and Observability

I'm not a physicist, but rather a control (feedback) systems engineer eager to understand more than just a cursory explanation of quantum mechanics. The StackExchange has been an excellent forum for ...
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0answers
154 views

What are you studying when you study a Harmonic Oscillator in QM?

This probably is a naive question - so please forgive a self-studier. In the text I am studying, one builds a HO by placing a particle in a potential that increases quadratically from the origin. The ...
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0answers
88 views

What is a continuous superselection sector?

I'm studying the terrible subject of continuous superselection rules and I faced with the following problem. Usually (continuous or discrete) superselection rules are defined involving a direct ...
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0answers
65 views

How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?

I really don't understand with the linearity conditions I have where this comes from.
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0answers
40 views

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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0answers
51 views

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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0answers
140 views

Direction vector of a physical quantity matrix

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 + ...