The tag has no wiki summary.

learn more… | top users | synonyms

8
votes
2answers
2k views

What is probability current in quantum mechanics?

What is probability current in quantum mechanics? Why define such a thing? I mean the meaning of probability current. I know the formula for it but I just don't get the idea of a flow of probability ...
3
votes
1answer
314 views

Earth still exists, does this fact tell us anything about LHC safety?

When LHC was about to be launched there were many fears that it would destroy the world, to counter them scientists tried to carefully examine all possibilities and concluded that there is nothing ...
0
votes
3answers
95 views

Why does Hamiltonian follow the property $H^*_{ij} = H_{ji} $?

I was reading Feynman's Lectures III's Hamiltonian Matrix. There I found this property of Hamiltonian Matrix: The Hamiltonian has one property that can be deduced right away, namely, that ...
0
votes
2answers
273 views

What do “ℜe” and “A*” mean?

What do "$\mathfrak{Re}$" and "A*" mean in the following equation (taken from James Binney and David Skinner's QM lecture notes, equation 1.12), \begin{align} p(S\text{ or ...
2
votes
2answers
114 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
1
vote
2answers
89 views

Why can the probability function for a particle in an infinite square well be larger than 1?

For a particle in a one dimensional infinite potential well of width $L$ the probability function is: $$P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ for $0\leq x\leq L$. The ...
-1
votes
0answers
30 views

Liouville's theorem in quantum mechanics

Is there any theorem in quantum mechanics which relates conservation of any physical quantity (say density) just like Liouville's theorem does in classical mechanics?
2
votes
1answer
96 views

Why electron can not be found at some node locations in the infinite potential well?

Consider electron in an infinite potential well, studied in quantum mechanics. Position probability density of the electron is $$ P_n(x)=\left(\frac{2}{L}\right)\sin^2\left(\frac{n\pi x}{L}\right)$$ ...
2
votes
2answers
152 views

What aspect of quantum mechanics forces probabilities to be (conventionally, at least) central?

I understand how to compute probability distributions and expected values and such from quantum states, but a lot of treatments of QM make it look like this is what the wavefunction is essentially ...
2
votes
2answers
117 views

Probability of fluorescence: matching of binding energy and incoming radiation energy?

Assume an X-ray diffractometer equipped with a copper anode X-ray tube. When a sample containing cobalt, iron, or manganese is irradiated by copper's K$\alpha_1$ radiation, sample fluorescence becomes ...
1
vote
3answers
107 views

Wave Function concept

What do we mean when we say wave function of electron? Does it mean wave nature of electrons? I am really confused.Without clearing this confusion i cannot proceed to molecular orbital theory.I am ...
4
votes
1answer
130 views

Probability density of detection of collinearly emitted photons in two detectors

Update: As proposed by @dmckee, I added equation numbers and improved the display of some equations. The answer by @Trimok inspired me to look at coordinate systems which are not specific to the ...
3
votes
3answers
183 views

How do probabilities emerge in the many-worlds interpretation?

My understanding is that at each quantized unit of time that a split occurs, every possible recombination of particles occurs in the 'objective' universe. If this is the case, what relevance to ...
5
votes
1answer
166 views

Which position and momentum distributions arise from some wave function?

Consider a particle in one dimension with wave function $\psi(x)$. The probability density function describing how likely it is to find it in a given position is given by ...
0
votes
2answers
96 views

Entropy and Gibbs Free Energy

I've been struggling with the notion of entropy and gibbs free energy for almost three days now. Different sources on and off the internet say different things about entropy. Gibbs Free Energy is ...
1
vote
0answers
60 views

Probability flux

I was reading a text on Quantum Mechanics in which it said that $$\int{d^3 x \, j(x,t)} = \frac{\langle p\rangle}{m},$$ where $\langle p\rangle$ is the expectation value of the momentum operator at ...
0
votes
0answers
11 views

Probability distribution of the decay of a single radioactive nucleus [duplicate]

A single radioactive nucleus has a constant probability to decay at any moment. Does this imply that the decay of the particle has a uniform probability distribution from the point in time of the ...
0
votes
1answer
53 views

Does Quantum mechanics predict (statistical) frequencies?

I began reading a book by Bricmont and Zwirn (Philosophie de la mécanique quantique, as yet not translated). In a note (page 4), Bricmont writes (translation mine): Probability is a theoretical ...
0
votes
2answers
66 views

Violation of unitarity: meaning and consequences

What is meant by unitarity and violation of unitarity of a QFT? For example, Fermi theory of beta decay is said to violate unitarity. How does violation of unitarity make a theory sick?
1
vote
3answers
444 views

Fermi-Dirac Statistics

In Fermi-Dirac statistics the probability of being in a certain energy state is $$f(E) = \left[1 + \exp\left(\frac{E-E_F}{k T}\right)\right]^{-1}$$ In the area that I'm looking at the texts always ...
2
votes
1answer
103 views

Ising model on lattices with (vertical side length) $\neq$ (horizontal side length)

Consider the Ising model with nearest neighbours interactions on a rectangular lattice $L\times M$. If $L=M$ (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit ...
0
votes
1answer
36 views

What is the unit of information as defined by information theory?

It appears to be defined by probability; however, does it have some unit that indicates its 'information level' in terms of probability?
1
vote
2answers
80 views

Why is probability of finding the electron at a certain point when one of the slits is closed $|\Psi|^2 $ & not $|\Psi|^2 dx$?

Let in a given physical condition, the wave-function to a particle be assigned as $|\Psi (x_i,0,0,t)|^2 dx$. Now, at the double-slit experiment , the probability of finding the particle at any $x$ ...
1
vote
1answer
65 views

What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent ...
0
votes
3answers
65 views

Probability density for wavefunction given as infinite superposition of eigenstates

How do we find the probability density as a function of (x,t), if the wavefunction is expressed as an infinite superposition of eigenstates? When the wavefunction is expressed as a superpostion of ...
0
votes
1answer
63 views

Probability density for momentum in Quantum Mechanics

In a book i found the following equations: $$ \phi(k)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \Psi(x,0)e^{-ikx}dx $$ and $$ \Psi(x,t)=\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty ...
0
votes
1answer
84 views

Problem with momentum values in a QM problem

I have the following equation of $Ψ$ around a ring (the particle is bound to move only on the ring): To visualize the state(it dies before L/2 if L=2πR): We can see from the first picture that ...
0
votes
1answer
50 views

Can binary sequences generated from ergodic maps be chaotic?

Chaotic Sequences of IID Binary Random variables with their applications to Communications and related papers by the same author, Tohru Kohda, talk about the statistical properties of binary symbolic ...
4
votes
2answers
359 views

Physical experiments - False positives

How is it made sure that something has been discovered, and not just noise? Is one discovery of something that is predicted considered to be enough (Higgs-particle)? What are the probabilities of a ...
1
vote
4answers
102 views

Importance of local conservation of probability

In almost every textbook of quantum mechanics we can find the derivation of the local conservation of probability. $$\nabla\cdot\vec{J}+\partial_t (\psi^*\psi)=0$$ where $\vec{J}$ is probabilty ...
0
votes
2answers
101 views

Regarding derivation of Probability Current

The question for the full derivation of Probability Conservation -> Probability Current was already asked here: Probability current. I apologize for not retyping it out, but it's already beautifully ...
1
vote
3answers
54 views

Calculating the probability of a given energy

Given a normalised wavefunction say $$\psi(x) = A\sin(n\pi x),$$ (where $A$ is a normalisation constant) I can calculate the probability of finding the particle being between a position $x$ and $x + ...
3
votes
2answers
149 views

Why does the magnitude squared of the wave function give us the probability density? [duplicate]

My question doesn't go much beyond the title: Why does $$\left | \psi \left ( x,t \right ) \right |^{2}$$ give us the probability density of something appearing at a certain location? I understand ...
0
votes
1answer
35 views

Calculating average quantities in kinetic theory

Consider a volume $V$ with $5$ particles each of mass $m$ at positions $\mathbf{q}_i=(x_i,y_i,z_i) \in V$ and with velocities $\mathbf{v}_i=(u_i,v_i,w_i)$. The speeds of the particles are between $0$ ...
30
votes
5answers
4k views

Why do all the atoms of a radioactive substance not decay at the same time?

Why does the substance decay at a rate which is proportional to the amount of the substance at that moment? As all atoms are in hurry to become a stable atom and as their decay do not depend on any ...
1
vote
2answers
45 views

Expansion of a ket-physical interpretation of coefficients

Consider I have a state represented by the Ket: $$|\psi\rangle=\sum_i a_i |\phi_i\rangle$$ What are the physical interpretations of the coefficients $a_i$? My guess is that $|a_k|^2$ represents the ...
2
votes
1answer
44 views

Cosmological fluctuations: what is gaussian?

When we are speaking about gaussianity and non-gaussianity in a cosmological context, what is gaussian or non-gaussian in the CMB? What would a non gaussian CMB look like compared to a gaussian one? ...
1
vote
1answer
31 views

What is the definition of 'relative population' in context of partition function?

In statistical mechanics, what is the definition (or mathematical definition) when authors refer to relative population in the case of a classical particle system?
0
votes
1answer
47 views

is it necessarily true that the partition function $Z$ (with degeneracies) $ =1$?

The partition function with degnerate energies is $$\text{Z}=\sum _ig_ie^{{-E_i}/{k_BT}}.$$ Because the partition function Z is defined as the normalisation constant, does Z always = 1?
4
votes
3answers
423 views

Are negativity of the Wigner function and quantum behaviour equivalent?

I've read the following question: Negative probabilities in quantum physics and I'm not sure I understand all the details about my actual question. I think mine is more direct. It is known that the ...
1
vote
1answer
82 views

Why is probabilty conserved under time evolution of a system in quantum mechanics?

I've studied quantum mechanics to a certain degree, but one question that I've never been able to get a fully satisfactory answer to is why probability is conserved (by this I mean that it has either ...
-1
votes
2answers
147 views

Why do termite pellets fall in a perfect circle?

I was just wondering why termite pellets fall down from my bed in a perfect circle. You can see from the images that the follow down on the floor making a perfect geometric figure which is void in ...
1
vote
2answers
190 views

Number of microstates compatible with two boxes

From my notes I have: From one point of view there are many more microstates compatible with the LHS than the RHS, in fact the relation between the number of microstates is ...
1
vote
2answers
2k views

The probability of finding the electron in the H-atom

In the book Arthur Beiser - Concepts of modern physics [page 213] author separates the variables in the polar Schrödinger equation assuming: $$\psi_{nlm}=R(r)\Phi(\phi)\Theta(\theta)$$ then there a ...
2
votes
1answer
67 views

Probability of photon emission

If a photon of a given wavelength is absorbed by an electron (for simplicity, let's assume the electron has only one excited state), does the probability that the electron jumps to its excited state ...
2
votes
4answers
611 views

Proof of Liouville's theorem: Relation between phase space volume and probability distribution function

I understand the proof of Liouville's theorem to the point where we conclude that Hamiltonian flow in phase-space is volume preserving as we flow in the phase space. Meaning the total derivative of ...
3
votes
2answers
161 views

Detailed balance condition for coupled Langevin equation

Suppose $a$ and $m$ are real variables and they satisfy the following two coupled Langevin equations: $$ \dot{a}=F_a(a,m)+\eta_a(t);\quad\dot{m}=F_m(a,m)+\eta_m(t); $$ where $\eta_a$ and $\eta_m$ are ...
1
vote
0answers
54 views

Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...
1
vote
0answers
76 views

What is a stochastic process in a physics context? [closed]

In my mind, a stochastic process is simply a "random" process, one where the outcome is informed by initial conditions but not in a deterministic way. Is this a correct definition? What are some ...
1
vote
1answer
85 views

Generalizing a Gaussian distribution

Perhaps this a nonsensical question but hear me out. I have a random variable $x$ whose moments I can calculate. The first moment $<x>$ is zero and the second $<x^2> = X^2$ is something ...