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Results tagged with quantum-mechanics
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user 43987
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.
1
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Multi-part Hamiltonian results in special properties of eigenfunctions?
No, for a number of reasons. Look at it from a discrete sense. Hamiltonians are Hermitian matrices. There are possibly infinite ways of writing a Hermitian matrix as a sum of two others. Also there is …
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Accepted
What is the probability of a system falling into an eigenstate after 3 measuremetns
Given: $$ |\phi_1> = \frac{1}{5} (3|\psi_1> + 4|\psi_2>)$$
$$ |\phi_2> = \frac{1}{5} (4|\psi_1> - 3|\psi_2>)$$
Your system in question starts at $|\phi_1\rangle$. Next we measure $d$. So there it ca …
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0
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A fixed number of fermions on a line
I am trying to work out a simple 1-D lattice model of non interacting fermions. In the simple case we have the Hamiltonian, $$ H = -J \sum_{x} a_x^\dagger a_{x+1} + a^\dagger_{x+1} a_{x}. $$
This …
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Uncertainty principle in Harmonic Oscillator
In a single particle Harmonic Oscillator, suppose I prepare it in the ground state and then measure its position. From the relation connecting Total Energy, Kinetic energy and Potential I can calculat …
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2
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Accepted
Prove that the elements of the dual frame of an IC POVM cannot be positive
Suppose $D_k \geq 0$ for all $k$. Notice that all the $D$ operators have unit trace.
For two PSD matrices it holds that, $Tr(AB) \leq Tr(A)Tr(B)$.
This implies that, $Tr(N_k D_k) \leq Tr(N_k)$ for all …
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1
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0
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74
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Practicality of measuring observables
In quantum mechanics Hermitian operators acting on the Hilbert space of a system are observables. From what I understand this means that there is some measurement we can do such that the eigenvalues o …
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Time evolution unclear
You seem to be making the assumption $e^{i(H_1 \otimes H_2)t} = e^{iH_1t}\otimes e^{iH_2t}.$ This is not true in general. Write down the spectral decompositions of the operators and then exponentiate …
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Question about tunneling diagram in adiabatic quantum computation
) The cost function is the spectrum of the final Hamiltonian. In fact the final Hamiltonian is often designed to solve some NP-hard problem like TSP or 3-SAT.
) This requires some explanation. The …
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10
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Why do we think Spin is angular momentum as opposed to some other quantity?
By treating spin as angular momentum a lot of phenomenon could be explained.
Conservation of angular momentum makes sense only if you include spin with the orbital angular momentum. Spin-orbit coup …
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5
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Physical meaning of $Tr(\rho ^2)$
If $\rho$ is the density matrix of a system then $Tr(\rho ^2) \leq 1$. If the equality holds the system is in a pure state and it is in a mixed state otherwise. But, what is the physical meaning of $T …
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Why is the Lagrangian approach preferred over the Hamiltonian approach in QFT? [duplicate]
Going from non-relativistic quantum mechanics(QM) to QFT there is a marked change in the approach used. QM almost exclusively uses Hamiltonains. Lagrangian based methods like the path-integrals are se …
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Few particle fermion system wavefuction
Suppose I have 3 fermions($\left|\psi_1\right\rangle$, $\left|\psi_2\right\rangle$, $\left|\psi_3\right\rangle$) and a system with 3 states ( $\left|1\right\rangle$, $\left|2\right\rangle$, $\left|3\r …
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Is the momentum of a particle both uncertain and, independently, also random?
Is momentum of a particle "random" because it is uncertain, or is it uncertain in addition to being random?
In quantum mechanics systems are represented using wave-functions (wave-vectors). The m …
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4
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Why hermitian, after all?
When in doubt go back to the masters. From Dirac's Principles of QM
When we make an Observation we measure some dynamical variable.
It is obvious physically that the result of such a measureme …
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4
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Adiabatic turning on of coupling constant in simulation of $\phi^4$ theories in the JLP algo...
In the Quantum Algorithms for Quantum Field Theories by Jordan, Lee and Preskill they have devised an efficient algorithm to simulate $\phi^4$ theories. Given by the Lagrangian density $$\mathcal{L}( …
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