Questions tagged [quantum-mechanics]

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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In quantum mechanics, why is information never completely lost?

In other words: in quantum mechanics, why are things considered as reversible? Is that a postulate?
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Can I define $\hat{x}$ as $x\delta(x'-x)$?

Operators can be thought of as matrices. Since matrices have two indices and involve summing: $A^i_j \psi^j\equiv A^i_0\psi^0 + A^i_1\psi^1 + A^i_2\psi^2 \dots$ and a summation between 2 vectors turns ...
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Understanding the phrase "Classical mechanics corresponds to the high frequency limit of quantum mechanics"

Recently I have taken an interest in mathematical physics and as my background is mostly in math itself, I have quite a lot of catching up to do regarding my knowledge of physics. One phrase that I ...
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In quantum tunnelling, what does actually propagate through the potential barrier: the wavefunction or the physical entity, which is described by it?

The wavefunction describes the quantum particle. The wavefunction exists on both sides of the tunnel barrier. It's the eventual detection on the other side that indicates the particle has tunnelled. ...
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How to find the second quantized form of Hamiltonian for particle in a box?

A single particle Hamiltonian can be written in the second quantized form as follows: $$F_{1}= \sum f_i(r_i,p_i)$$ $$F_1=\sum(l|f_i|l')a_{l}^{\dagger}a_l$$ When we use this for the hamiltonian of a ...
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If object (as tennis ball) can't be described by one wavefunction, how can we say there's non-zero probability for quantum tunnelling of such object?

A "macroscopic" object (e.g. a cup) cannot be described by one wavefunction (in the sense of a solution of ONE quantum mechanical equation). And even though the object can be described by ...
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How shift the system Hamiltonian change the interaction term?

I'm reading this paper about a model of a qubit coupled to an Ising spin bath. The interaction between the system qubit and the bath is described by the Ising Hamiltonian: $$H_{I}^{\prime}=\alpha \...
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How can I actually get to the AKLT state from a product state in finite depth?

I'm currently learning about symmetry-protected topological phases in one dimension. The ground state of the AKLT model provides one such example. In particular, the AKLT state for any length $L$ ...
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Papers of real experiments measuring momentum of individual particles?

I am trying to understand the different methods that have been used to measure the momentum of individual particles. I have been able to find a few methods (with corresponding papers describing the ...
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Kitaev Chain - Obtaining a real-orthogonal matrix that block-diagonlises the Kitaev Chain

I encounter a subtle problem regarding the Kitaev Chain. In Kitaev framework, he tried to express the Hamiltonian into real-orthogonal basis. Suppose the Majorana system is described by $$ H = \frac{i}...
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According to quantum mechanics, can a "macroscopic object" (e.g. tennis ball) spontaneously get in coherent state?

According to quantum mechanics, can a "macroscopic" object (e.g. tennis ball) spontaneously and without any manipulation/intervention get in coherent state?
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Quantum Harmonic Oscillator density matrix in coherent states base

I was trying to calculate matrix elements of the density operator for a 1D QHO (with Hamiltonian $\mathcal H = \hbar\omega a^\dagger a $) in the base of coherent states $\{\vert\alpha\rangle\}$ and ...
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Minimal condition(s) for the emission of a photon to occur

I was working out a practice problem where you needed to give all the possible states (where the emission of a photon occurs) of a H-atom at excited 5d state. So I started by whriting down all the ...
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Regarding two-particle interferometry and single-detector probabilities, Horne/Zeilinger (1989)

I was reading Horne, Shimony, Zeilinger "Two-Particle Interferometry" from 1989, an article showcasing how momentum-superpositioned particle pairs from a down-conversion crystal can lead to ...
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Are electric force and strong force equal in magnitude?

Should the electric force and the strong force be equal for a nuclei to be stable? Because if perhaps, the strong force is now more than that of the electric force, then shouldn't the nucleus collapse ...
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Is there isomorphism between monopartite and bipartite quantum system?

I know the definition of monopartite, bipartite quantum system and the fact that they are defined as Hilbert space. And I also find the theorem that any two Hilbert spaces which have the same ...
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Stern-Gerlach experiment

In the Stern Gerlach experiment, one can determine the value of $j$ (eigenvalue of $J^2$) by counting the number of discrete lines formed on the screen. For instance, if I count 7 discrete lines on ...
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Where did I go wrong in separating the Hamiltonian? [closed]

I am trying to show that the Hamiltonian of a two-body system can be rewritten in the form $$\frac{\textbf{P}^2}{2M}+\frac{\textbf{p}_{\text{rel}}^2}{2\mu}+V(\textbf{r}_1,\textbf{r}_2),$$ (where $\...
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Classical Mechanics Lagrangian from Underlying Quantum Field Theory

Does the K - T classical mechanics Lagrangian emerge from some structure of the Lagrangian of the underlying QFT?
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Understanding Gaussian ground state wave functional

Right now I'm looking into Gaussian state preparation for quantum simulation of field theories. These Gaussian states are important because they are the ground state of the free fields of interest. I'...
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Position Eigenstates of Harmonic Oscillator Using Squeeze States

Ultimately, I want to establish a relationship between an eigenstate of position and an energy eigenstate of a harmonic oscilator. If we take the squeezing operator and let $ \gamma \rightarrow \infty$...
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The double slit experiment from the path integral approach

I am reading the book Topics in Advanced Quantum Mechanics by Holstein. In Chapter 3, section 3 he discusses the Aharonov-Bohm effect, but before doing so he discusses the ordinary double slit ...
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Relation between diagonal and off-diagonal entries of Hermitian Operator

I am started doing a project in Quantum Chemistry and stumbled upon a problem which I can not seem to find the answer to. As the title suggests, I am looking for a relation between the diagonal and ...
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Doubt regarding transitions in Time Dependent Perturbation Theory

In Time-Dependent Perturbation Theory, One deals with the problem of transition from an initial state that is part of a discrete spectrum, to a continuum of states, now certainly the state space of ...
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What will happen if one used $[\phi (x), \frac{\partial L}{\partial (\partial _x\phi(x))}]=i\hbar$ to get a Quantum Field Theory?

Classical field theory does not discriminate between space and time, but canonical quantisation does. We use the relation $$[\phi (x), \frac{\partial L}{\partial (\partial _t\phi(x))}]=i\hbar$$ to get ...
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Acoustic absorption coefficient of Metals

Which non toxic Metals have the lowest Acoustic absorption coefficient?
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electronic conductivity in superconductors

In studying simple drift based conductivity in metals and semiconductors, we follow the simplistic drift based model wherein, $$J = e(n\mu_n + p\mu_p)E = e(nV_{d,n} + pV_{d,p})$$ This is a completely ...
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A specific question about sakurai modern quantum mechanics

In the kronocker deltas for spin, $\lambda_4$ and $\lambda_3$ places changes. How can the author change their places? Also, I see both case can appear by calculation so there are two different ...
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Are there wave functions that are neither symmetric nor antisymmetric?

While proving the Pauli Exclusion Principle, one has to show that the wave function is antisymmetric for fermionic particles: $$\Psi(x_1,x_2) = -\Psi(x_2,x_1)$$ Which is typically derived from ...
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Experimental Justification for envelope function approximation

The traditional device picture for describing electron dynamics in conduction bands of semiconductors and heterostructures uses Envelop Function approximation (EFA). The EFA assumes the external ...
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Are there things with different physical attributes that serve exact same purpose in a system? [closed]

I’ve been puzzling about this cross-disciplinary concept for the last week. Can you think of any two things that have different physical make up that serve the exact same purpose? For instance, ...
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1 answer
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$(a - a^t)e^{\frac{1}{2} a^ta^t} | 0 \rangle = 0$ [closed]

When talking about the limits of squeezed states, we reach the conclusion that $e^{\frac{1}{2} a^ta^t} | 0 \rangle$ must be an eigenstate for momentum since the uncertainty in momentum becomes zero. ...
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Quantum rigidity and zero-point energy

I am currently going through the Nature review on cuprate superconductors by Keimer at all and I am having a bit of difficulty understanding this sentence, which is located near the top of page 181: ...
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Condition for an operator on a quantum Hilbert space to behave like vector

In QM we work with $H=L_2(\mathbb{R}^3)$ as a Hilbert space of square-integrable complex-valued functions. Now we define a special set of three operators $L_x, L_y, L_z$ by $L_i = \varepsilon_{ijk} \...
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Type of energy in energy band diagram of a solid

What type of energy do the energy levels in the energy band diagram of a solid such as silicon (Si) represent? potential energy? kinetic energy? or total energy? I saw in a book that kinetic energy of ...
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Why can the orbital quantom number $l$ take on half integer values? [closed]

In Griffiths' "Introduction to quantum mechanics", the author shows in chapter 4 that the orbital quantum number $l$ can take on half integer numbers. This is shown using Dirac's lowering ...
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Can we use entangled particles to find out what is going on inside a black hole?

If you throw one entangled particle inside a black hole can we know what is happening with it from looking into another entangled particle outside the black hole?
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Omitting the negative exponential in the plane-wave solution of the Schrodinger equation

The time-independent Schrödinger equation in one dimension for a free particle, $$\frac{-\hbar^{2}}{2 m} \frac{\partial^{2} \Psi(x)}{\partial x^{2}}=\varepsilon\Psi(x)$$ can be solved as a homogeneous ...
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Probability for an Energy measure of a quantum state [closed]

I'm stuck on a request in a problem about Quantum Mechanics. The problem starts by giving the ket of an harmonic oscillator $1D$: $$|z\rangle = \sum_{n = 0}^{+\infty} |n\rangle \frac{z^n}{\sqrt{n!}} \...
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Is spin angular momentum per unit mass AKA specific spin angular momentum used outside of quantum mechanics?

A siderostat is an object (a device, normally) that has a constant orientation with respect to the "fixed stars", or rather with respect to the distant galaxies. An example would be a ...
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Why does the Planck curve drop below the Rayleigh-Jeans curve for blackbody radiation when Planck quantized the energy?

This has been a research topic of mine for days now. I understand the Rayleigh-Jeans law and how it leads to the ultraviolet catastrophe. I have been searching for a clear, conceptual explanation of ...
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Look this is simple I'm They've forgotten to calculate for the background radiation in the slit experiment [closed]

Not gonna go in deep because better people are gonna have to do the math but the back ground radiaiotn found by bell labs is what is causing the diviation in the slit experiment.
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Do electrons combine to form a single particle

I was reading about exchange interactions and stumbled across this website that was discussing symmetry and the exchange interaction. The website stated The exchange interaction is originated from ...
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Question about quantum mechanics / harmonic oscillator

In shankar's book when treating the harmonic oscillator hamiltonian In the step inside black rectangle why he worte the operators $$X^2 , P^2$$ As product of two dagger and non dagger operators $$X^+...
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Why do we need Quantum Gravity [duplicate]

I know this question has been asked many times but I have not found a satisfying answer to it yet. I understand Gravity as an emergent phenomenon of mass/energy. I understand quantum mechanics as the ...
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1 answer
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Could there be a Planck sized black hole with positive charge in the center of each atom, moving so fast on its way that it has nearly any mass?

Days ago I made a post asking if it would be possible to find a Planck sized black hole in the center of each atom. I was told the Planck mass is much heavier than an atom. Finding a way to have all ...
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1 vote
2 answers
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Understanding dot product in quantum mechanics [closed]

Let's say we have a two-state-system with state $\vert 1\rangle$ and state $\vert 2\rangle$. From my understanding one can assume the base vectors of this system to be $\vert1\rangle \mapsto (1,0)^\...
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How to understand the action of functions of Pauli Matrices on qubits? [closed]

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ In the attached photo, my professor has evaluated the action of the exponential of the x and y Pauli matrices on z-basis eigenstates, and there ...
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Help with expanding to second order in perturbation theory

In McIntyre's Quantum Mechanics: a Paradigms approach (pg 318), we solve for the energies of a perturbed 2 level system to get that $$E_1= E^{(0)}_1+\lambda H'_{11}+\frac{\lambda^2|H'_{12}|^2}{(E^{(0)}...
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Definite energy states for ammonia molecule (Feynman Lecture Volume III Chapter 9.1)

I have a question regarding this text passage of the Feynman Lecture Volume III chapter 9.1: Here $C_1$ and $C_2$ are the amplitudes for the ammonia molecule either beeing in state 1 or state 2. ...
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