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 ...

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Anti-particle problem for Dirac sea

According to the Dirac hole theory we know that Dirac sea is completely filled with negative energy, called vacuum. We will need $2mc^2$ or greater to get electron and a positron by incident photon. ...
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Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $

I have come across the equation which comes out of the nothing in Zettili's book Quantum mechanics concepts and applications p. 167: $$\psi(\vec{r},t) ~=~ \langle \vec{r} \,|\, \psi(t) \rangle.$$ ...
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504 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
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Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
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172 views

Expectation value - Zetilli vs Griffith

I know that an inner product between two vectors is defined like: $$\langle a | b\rangle = {a_1}^\dagger b_1+{a_2}^\dagger b_2+\dots$$ but because a transpose of a component for example $a_1$ is ...
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133 views

Observables - what are they?

I often read in books that an observable is represented by an Hermitean operator. But it is deceiving as operator isn't the observable. As far as I've read the observable is denoted like $\langle ...
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314 views

Wigner characteristic function

I came across the "representation of a Gaussian state by its Wigner characteristic function". I don't know what Wigner characteristic function is and google results are not precise enough. Neither ...
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1answer
138 views

Geometrical Representation Grover algorithm

I am studying the Grover algorithm and in my and others lectures, I've come across this picture. If the dimension of the computational basis is greater than 2, why does the evolution algorithm ...
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82 views

Why Quantum correlation is not uniform in this diagram?

Following diagram is from a Wikipedia article which shows Quantum Correlation for local hidden variables and Quantum Mechanics and experiments confirm Quantum Mechanics predictions. My question is ...
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54 views

Is it possible to detect subjective decoherence? If yes, how?

In his paper from 1994 Thomas Breuer describes a phenomenon of subjective decoherence (p. 43). I wonder whether it can be measured, and if yes, how. I also wonder whether it would allow to create an ...
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830 views

Is particle entanglement a binary property?

Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are ...
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Using the Normalization Condition with Wavefunction

I'm very confused with this problem and I was looking for some guidance. $$\psi(x) = Ae^{ikx}e^{-x^2/2a^2}$$ Use the normalization condition to find A. So I understand that you use the normalization ...
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79 views

Can a link between photons that don't exist at the same time provide communication with the past?

They have published something about a link between photons that don't exist at the same time. Does this means that it is possible to build a device that will receive messages from itself but these ...
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480 views

How do you come up with a POVM?

This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me. Say you have a physical quantity $E$ that can take values 1, 2, 3 ...
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76 views

Frank Hertz experiment and different jumps

Why is it assumed that in this experiment, the jump will be between the second and the first states. Couldn't it be that when the electrons have enough energy, an atom absorbs enough to get to the ...
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154 views

Time evolution of a quantum state

I have another point in QM that I would like clarified. Suppose $$\{|n\rangle\}$$ is a set of eigenstates of both the Hamiltonian $H$ and another operator $\hat O$ corresponding to an observable also. ...
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353 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
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148 views

Can we apply de Broglie's relations to sound waves?

Can we apply the de Broglie relations to a sound waves ? Is it possible? if yes how do you do that? what would be the mass(m) in the equation?
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Clarification on measurement in QM

Supppose we are given a quantum state that isn't pure state, such that it is a linear combination of the eigenstates of a Hermitian operator $\hat O$. $$|\psi\rangle=N\sum \alpha_i |i\rangle$$ where ...
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388 views

Quantum Field Theory and Hilbert space dimensionality

Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis. How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
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451 views

Hilbert space of a free particle: Countable or Uncountable?

This is obviously a follow on question to the Phys.SE post Hilbert space of harmonic oscillator: Countable vs uncountable? So I thought that the Hilbert space of a bound electron is countable, but ...
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127 views

Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...
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Quantum mechanics and everyday nature

Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.
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763 views

Interpretation of de Broglie wave

Until what point can the de Broglie wave be thought as a real wave? I mean, is it made of something? What amplitude does it have? Is it a sine wave? How can it be related to the wavefunction of the ...
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216 views

What is the reason that relativistic corrections for hydrogen atom work?

Here I cite part from Sidney Coleman's lectures on Quantum Field Theory: It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
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Calculating the the kernel using path integrals for quadratic lagrangians

I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
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fast quantum random number generator + limited decoherence rate => Schrödinger cat state?

Suppose that fast quantum random number generator (QRNG, https://qrng.physik.hu-berlin.de/) is placed in a subsystem which has limited interaction with the rest of the world. What would happen if ...
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70 views

Eigenvector Grover Operator

I have a question about the eigenvectors for the evolution operator of Grover's algorithm. Let $U=R_DR_f$, where $$\begin{align*} R_D &= 2|D\rangle\langle D| -I_N , \\ R_f &= ...
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88 views

Eigenvalue $a_n$

Q1: In Zetilli's book page 166 (ch. "Postulates of QM", eq. 3.1) i encountered an expression $\hat{A}|\psi\rangle = a_n|\psi_n\rangle$. I know this is an eigenvalue equation, but i have seen another ...
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63 views

Scalar-fermion bound state

Is it possible to have a bound state between a scalar and a fermion? For example, a squark--anti-squark bound state, provided that the decay width is sufficiently small compared to the binding energy? ...
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182 views

Why is this not a realisable operation on a quantum system?

Let $\rho = \begin{bmatrix}\ 1&0 \\ 0&0 \end{bmatrix}$, $\rho' = \begin{bmatrix}\ 0&0 \\ 0&1 \end{bmatrix}$, $\rho'' = \dfrac{1}{2}\begin{bmatrix}\ 1&1 \\ 1&1 \end{bmatrix}$ ...
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1answer
128 views

Uncertainty Principle on System of particles

I am new to Quantum Mechanics. I read the uncertainty principle - it says there are pairs of physical quantities which can't both be determined with certainty for a particle. My question is does the ...
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400 views

Some Dirac notation unclarities

Q1: Ok so i have come to a point where i know that $\Psi(r,t)$ which we denote only by $\Psi$ can be represented in a Hilbert space by a vector which we denote $\left|\Psi\right\rangle$. Does this ...
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Hamiltonian in 2-dimensions? [closed]

I am trying to construct a Hamiltonian for a system in 2 dimensions using Matlab. I am not sure how this Hamiltonian will look like in matrix form. If somebody can help me visualize this matrix that ...
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253 views

Why is the Heisenberg Uncertainty Principle not obvious give the conservation of mass- energy?

A photons energy is given by $E=h *f$ and momentum $p=E/c$ (spin?) but the photon has no (rest) mass! Therefore it is the ultimate probing tool for looking at any mass position and velocity because ...
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420 views

Can we measure “wavefunction” of quantum particles?

We know that there is uncertainty principle, so question: can we ever measure wavefunction of particles? I do not think this is possible, but I am not sure. I guess that everything is probabilistic. ...
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478 views

what is the magnetic quadrupole operator?

To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
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476 views

What is the magnetic quadrupole moment of a nucleus in cylindrical coordinates?

What is the magnetic quadruple moment of a nuclei in cylindrical coordinates? The quadrupole moment of a nucleus is zero in spherical coordinates but in the cylindrical coordinates it can't be ...
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Periodic boundary condition on a Wave Function of a Particle in a Box

Until now solving the Schrodinger Equation for a particle in a box was relatively easy because the boundaries conditions imposed zero value on the wave function at the boundaries. But now I must find ...
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234 views

Quantum Mechanical Operators in the argument of an exponential

In Quantum Optics and Quantum Mechanics, the time evolution operator $$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$ is used quite a lot. Suppose $t_i =0$ for simplicity, and say the ...
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186 views

Vector $\vec{z}$ and its conjugate transpose $\overline{\vec{v}^\top}$ - is it the same as $\left|z\right\rangle$ and $\left\langle z \right|$

Lets say we have a complex vector $\vec{z} \!=\!(1\!+\!2i~~2\!+\!3i~~3\!+\!4i)^T$. Its scalar product $\vec{z}^T\!\! \cdot \vec{z}$ with itself will be a complex number, but if we conjugate the ...
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How do particles become entangled?

A person asked me this and I'm just a lowly physical chemist. I used a classical analogy (how good or bad is this and how to fix?) Basically, light has a net angular momentum of zero, insofar as ...
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520 views

Is every quantum measurement reducible to measurements of position and time?

I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
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326 views

Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
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120 views

Is it possible to use quantum mechanics for an effective time based encryption?

This is for an application in cryptography. There is a concept called "time based cryptography", where a message can be decrypted only after a certain time, Say "12/12/2060, 12:30 GMT". There are some ...
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Time evolution of Gaussian wave packet

I'm slightly confused as to answer this question, someone please help: Consider a free particle in one dimension, described by the initial wave function $$\psi(x,0) = ...
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Hilbert space of harmonic oscillator: Countable vs uncountable?

Hm, this just occurred to me while answering another question: If I write the Hamiltonian for a harmonic oscillator as $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$ then wouldn't one set of ...
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Question regarding operators and cylindrical coordinates

I have the following problem in my hand: I need to arrive from the Cartesian expression $$x_{j}{\partial_{k}}x_{j}{\partial_{k}}-x_{j}{\partial_{k}}x_{k}{\partial_{j}}$$ to this expression: ...
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Does quantum mechanics depend solely on electromagnetic waves? [duplicate]

I am beginning to learn quantum mechanics. Since determining the position of an object involves probing by electromagnetic waves and since i have read a simple derivation of Heisenberg's uncertainty ...
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150 views

Matrix representation of state

This is a quantum mechanics question, I don't quite understand what it's getting at... Suppose the we have a state described by $|1\,\,\, m\rangle$. Let its matrix representation be $\vec u$. ...