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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23 views

Is the spectrum of a product of two operators, $AB$, invariant under $UAU^{\dagger}$ for unitary $U$?

This question is about linear operators on a Hilbert space. If necessary, the Hilbert space can be assumed to be finite dimensional. I have two Hermitian operators, $A$ and $B$. Do we have $$ ...
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30 views

Algebraic formulation of quantum mechanics and unbounded operators

Posted in the physic site: In AQFT one specifies the structure of the observables as a $C^*$-algebra. This seems to excludes algebras that don't have a norm, such as the Heisenberg algebra. ...
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28 views

Homeomorphism between the space of all Ashtekar connections and spacetime?

This is a question I've asked in physics.stackexchange: Excerpt from an essay of mine: Let $\Psi(\varsigma)$ be the wavefunction in the loop representation, where $\varsigma:[0,1]\to\mathcal{M}$, ...
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47 views

Question arising from quantum mechanics concerning groups and symmetries

I'm trying to understand a calculation my professor did in my quantum mechanics script. Here it is: Each rotation $R \in O(3)$ induces a unitary transformation in $L^2(R^3)$, i.e. the space of square ...
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19 views

Could anyone help me differentiate an ansatz for the Calogero-Marchioro model?

Could anyone help me substitute the following ansatz, $$\psi=(\prod_{i<j}^{N}\bf{r_{ij}^{2}})^{\frac{\Lambda_D}{2}}\phi(p)$$ into $$H=-\frac{{\hbar}^{2}}{2m}\sum_{i=1}^{N}{\nabla}_i^{2}$$ So ...
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1answer
43 views

the split of two quantum dice

We need to find the probabilities of the sum and the difference of two quantum dice. What is the probability of their sum to be 2? it can be accomplished only when both dice are 1. the probability of ...
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31 views

Oscillator solutions with regard to TDSE Eigenvalues

Taking a shot at a QM harmonic oscillator problem tonight. Consider a 1-D harmonic potential: $$ V(x) = \frac {m\omega^{2}x^{2}} {2} $$ solve for the gen. solution to the TDSE, $ \psi(x,t)$ utilizing ...
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57 views

Quantum Mechanics Angular Momentum Bra-ket notation

Show that if the state $$ \rvert\gamma\rangle $$ Is real then the expectation value of each component of the angular momentum is zero. Does this imply theangular momentum is zero? My Work: $$ ...
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1answer
45 views

Proof that $\langle[\hat{H},\hat{O}]\rangle=0$

How can I show that for a particle in an infinite square well in a stationary state, that the expectation value $\langle[\hat{H},\hat{O}]\rangle=0$ where $\hat{H}$ is the Hamiltonian operator and ...
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0answers
23 views

Commutation with a Hamiltonian analogue

I've been given the problem of showing the following commutation; $$[A_{j} , H] = 0$$ With $H = \frac{p^2}{2m} - \frac{Ze^2}{r}$. Now, I'm assuming that the $A_j$ are Runge vectors (but, they might ...
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1answer
59 views

Angular Momentum commuting with Hamiltonian

I've been given an assignment where I have to prove that the angular momentum operators $L_j = \varepsilon_{jkl}q_{k}p_{l}$ commute with the Hamiltonian, given as $H = \frac{p^2}{2m} + V(r)$. Now, I ...
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64 views

Topic/Book recommendation for a reading course about quantum mechanics/field theory/information

I am currently studying mathematics in the 5th semester and at my university, we are offered something called a "reading course", where a student will have to read a/several book/s about a topic he is ...
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2answers
88 views

How does one simplify exponents for complex primitive nth roots of unity?

Let us define a complex primitive N-th root of unity, omega: $$ \omega = \cos(\theta) + i\sin(\theta) \\ = e^{\frac{2\pi}{N}} $$ By the definition of an nth root of unity, ω is the second solution to ...
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0answers
11 views

Approximations for the Coarse Graining of the one norm difference of two probability distributions

I want to coarse grain $D(P_{1},P_{2}) = \frac{1}{2} \sum_{r}^{D} |Pr(r|1) - Pr(r|2) |$ for two distinct distributions Pr(r|0) and Pr(r|1). Such that $\sum_{r} P(r|1) = 1$ and $\sum_{r} P(r|2) = 1$. ...
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127 views

Symmetry adapted basis function to make the Hamiltonian matrix Block Diagonal.

Can anybody give me a tip to solve this problem? I have large quantum mechanical Hamiltonian, to solve it numerically I have to decompose it into the block diagonal form. To convert the hamiltonian ...
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0answers
57 views

Quantum mechanics/Probability Question?

I have a 6 question homework from my Quantum Mechanics Class and I solved most of it (or at least attempted most of it). This one however is tripping me up. Any help would be appreciated. A 3D ...
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0answers
148 views

Schwinger's Oscillator model of Angular Momentum and irreducilbe representations

I don't quite understand the connection between the final result attained by Schwinger in his oscillator model for angular momentum. Can any one help me understand how we get an " irreducible ...
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1answer
37 views

Determinant Expression for Grover operator

I want find the characteristic polynomial for the grover quantum operator $U^{N\times N}$ $$\begin{align*} U=(2|D\rangle\langle D| -I_N)(2|M^{\perp}\rangle\langle M^{\perp}| -I) \end{align*}$$ ...
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1answer
59 views

Dirac's notation? (QM)

I have a question regarding Dirac's notation in quantum physics. As far as I understand: $\langle a|b\rangle=(a1^*,a2^*)*(b1,b2)^T$ But what does $\langle1/2,1/2|J|1/2,-1/2\rangle$ mean?
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3answers
176 views

Quantum uncertainty can explain the Riemann Hypothesis?

In the recent paper "Riemann Hypothesis as an Uncertainty Relation" (http://arxiv.org/abs/1304.2435) the author claims that the presence of zeros out of the critical line may lead to the violation of ...
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1answer
91 views

Qubit state finding [closed]

Suppose we have two qubits in the state $x|00\rangle+y|11\rangle $. What is the resulting state of the second qubit in that case? Use and to denote and respectively.
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Reversing Summation and Product of Sequences [closed]

I am working on a proof for some homework, so I will leave all details out. I can prove it if this step is mathematically sound: ...