# Tagged Questions

For questions on quantum mechanics, a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.

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### Why the principal quantum number (n) is maximum 7? [closed]

Can you explain why actually the principal quantum number is maximum 7?
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### Properties of Hermitian matrices

Consider hermitian matrices M1, M2, M3, M4 that obey the property Mi Mj + Mj Mi = 2δij I where I is the identity matrix and i,j=1,2,3,4 a) Show that the eigenvalues of Mi=+/- 1 (Hint: Go to the ...
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### Compatible Hilbert space subspaces - need help understanding a statement made in a book

A book I'm reading has the following in a section on lattices formed by subspaces of a Hilbert space : Two subspaces $M$ and $N$ are compatible if there exist three mutually disjoint subspaces ...
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### Double-commutator $[f,[f, - \Delta]] = -2 |\nabla f|^2.$

This book (proof of Theorem 3.2) in chapter 3.1 claims click me that an easy computation shows that $$[f,[f, - \Delta]] = -2 |\nabla f|^2.$$ where $[.,.]$ denotes the commutator. Unfortunately, I ...
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### Perturbation theory, why are the assumptions of the method satisfied?

I am a undergrad student interested in math taking quantum mechanics. Yesterday I was introduced to what physicists call perturbation theory, non-degenerate case. According to authors Griffiths, ...
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### Entanglement and linear algebra

How do you represent entanglement of two particles in quantum mechanics using linear algebra? How does measure of one particle affecting the state of other quantum mechanically captured linear ...
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### Deutsch–Josza algorithm in Hilbert spaces

What would be the construction of Deutsch–Josza algorithm in Hilbert spaces, e.g. With white noise analysis?
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### The probability of measuring the control qubit in zero in a quantum circuit

I’m working on an assignment where I have to solve some questions about a quantum circuit. In particular, I have a quantum circuit with three qubits: $|0\rangle$(referenced to as the control qubit), ...
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### Make mathematical sense of the Dirac well Potential Equation

A classical problem in quantum mechanics involving the Dirac Delta function is given by $$y''+(\delta(x)-\lambda^2)y=0$$ Then, to find ''bound states'', you solve on the right and find the ...
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### On block density matrices and CPTP maps

Consider a $n\times n$ density matrix $\rho$ and decompose it as $$\rho=\left[\begin{array}{c|c} \rho_A & \rho_B \\ \hline \rho_B^\dagger & \rho_C\end{array}\right],$$ with $\rho_A$, ...
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### Why $|j_1 - j_2 | \leq j \leq j_1 +j_2$ holds for $J= J_1 +J_2$, the addition of angular moment?
I wonder why the total angular momentum $$J=J_1 +J_2$$ is given in the range of $$|j_1 - j_2 | \leq j \leq j_1 +j_2$$ Of course we can verify this in the course of finding Clebsh-Gordan ...
I am reading the book of Albeverio named Solvable models in quantum mechanics. In the first chapter it is explained how to realize the operator $"-\Delta+\delta_0"$ as a self adjoint operator on ...