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Results tagged with quantum-mechanics
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user 250506
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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Wavefunction used in Derivation of Josephson Effect
I guess the main point is that in some ordinary material you have no such collective behavior as in a superconductor, which allows you to describe all electrons within your material using only one coh …
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Does the Bell test preclude localism, realism, both, or just one of either (indeterminate)?
The violation of Bell inequalities proves that quantum mechanics is incompatible with the assumption of local realism (rather than with the assumptions of locality and realism), in the sense that eith …
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What is the difference between pure Bell states and Bell mixed states?
I would not say “something changes”. Basically any kind of joint or local measurements is performed by means of the same experimental setups. What rather changes is the mathematical description of you …
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2
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Kraus decomposition
As the derivation you are looking for is not that hard, I guess your confusion probably follows from the fact that your notation does not label states as belonging to the Hilbert spaces $\mathcal{H}_A …
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Accepted
Energy measures and probability of measuring them
Yes, you are right. First of all about the fact that the only allowed measurement outcomes for an energy measurement are the eigenvalues of $\hat{H}$, $a$ and $-a$, regardless of the time instant in w …
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What does it mean to expand a function in its basis?
From a physical point of view, you are always interested in observables, which you describe quantum mechanically by means of some hermitian operator. In fact, a property of Hermitian operators is havi …
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Accepted
Quantum Computation and Quantum Information - Exercise 4.16
Yes, your answer is correct.
A more straightforward approach would take into account the tensor product structure of the two-qubit wavefunction. In fact, the Hilbert space $\mathcal{H}$ for joint sta …
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0
answers
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Schmidt decomposition of bipartite states
When performing the Schmidt decomposition of a bipartite state $\left|\psi\right>_{AB}=\sum_{ij}c_{ij}\left|v_i\right>_{A}\left|w_j\right>_{B}$ is computing the eigenvectors of the reduced density mat …
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Classical vs quantum definition of observables
The fact that your probability distribution is sharply centered around the zero actually restricts the range of possible outcomes for a measurement of the particle’s position. As a consequence, the st …
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Energy expectation values in quantum mechanics with the provided spatial wave function
The energy expectation value is given as
$E=\langle \hat{H} \rangle= \int dz \psi^{*}(z)H\psi(z)$.
However, I don’t see how this should be related to the momentum expectation value in what you called …
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3
votes
Accepted
Strange use of the mean value into the definition of operators
What is meant by that expression is
$\Delta\hat{x}=\hat{x}-\langle\hat{x}\rangle \text{Id}$,
with $\text{Id}$ being the identity operator.
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2
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Accepted
Turning a bra made up of a tensor product of two bras into a ket (and vice-versa)
If you are dealing with a composite system as it seems, you don’t need to change the order of $\psi$ and $\phi$ from (1) to (2), since the first (second) ket/bra always refers to the first (second) su …
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5
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Operator norm and Action
The sup in the equation is a supremum over all states out of the Hilbert space $\mathcal{H}$. In other words, you pick the state $|\psi\rangle$ out of $\mathcal{H}$ for which the number $\frac{\mid\mi …
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Accepted
Bloch sphere representations for multi-qubit quantum systems
Let's denote the operators you wrote as $\hat{x}$, $\hat{y}$ and $\hat{z}$ as $\sigma_x$, $\sigma_y$ and $\sigma_z$, respectively. Then $\rho=\frac{1}{2}(I+\sum_{i=x,y,z}r_i\sigma_i)$, as I recall an …
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How do I write the matrix for the operator $\hat{S_y}$ in the basis $\{|{↑}_x⟩ , |{↓}_x⟩\}$?
The four matrix elements you are looking for are
$$
\langle {\uparrow}_{x} |\hat{S}_{y}| {\uparrow}_{x} \rangle, \
\langle {\uparrow}_{x} |\hat{S}_{y}| {\downarrow}_{x} \rangle, \
\langle {\downarro …
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