2
votes
2answers
36 views

How will a particle with energy less than $V_{\rm min}$ behave?

Consider e.g. the finite square well: $V = -V_o$ between $x=-a$ and $x=a$, $V=0$ elsewhere Now for scattering states, $E$ must be $> 0$. For normalizable bound states, $E$ must be $< 0$ and ...
0
votes
2answers
40 views

Total energy of a quantum gas

I'm dealing with a quantum gas, thought as a system of N non-interacting particles. I would be tempted to say that the total energy of the system equals the sum of the energies of the single ...
6
votes
1answer
102 views

What are the restrictions on the Hamiltonian in QM?

In quantum mechanics, we usually write the Hamiltonian as: $$\hat{H}=\hat{T}+\hat{V}$$ But in classical mechanics, there are several reasons why it would not have this form: We've chosen some ...
1
vote
1answer
70 views

When do we see particles to be in a superposition of energy states?

I have two doubts: Exactly when does this happen? and If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3? ...
0
votes
0answers
51 views

Questions on electron orbits

I have three questions to ask: Why do electrons (in an atom) specifically move in orbits and not some other type of motion? Where does the energy comes from, for the electron to move at much higher ...
13
votes
4answers
347 views

Why not drop $\hbar\omega/2$ from the quantum harmonic oscillator energy?

Since energy can always be shifted by a constant value without changing anything, why do books on quantum mechanics bother carrying the term $\hbar\omega/2$ around? To be precise, why do we write $H ...
0
votes
1answer
35 views

Relation between different quantum excitation energy, mass energy and kinetic energy

When a particle enters an excited state, the energy appears in its quantum wavefunction according to $E = h \nu$. Does the $E$ in this equation also include kinetic energy, and rest mass energy? ...
1
vote
0answers
28 views

How does a complex wavefunction “hold” energy?

Feynmann Lectures Vol 3 Ch 8 Sec 6 describes how an ammonia molecule can have two definite energy states. If the amplitudes of the base states are $ C_1(t) ...
1
vote
2answers
69 views

What causes different decays?

Nuclei spontaneously decay according to a certain decay rate. There are however different kinds of decay, alpha, beta, gamma... What causes then the nuclei, when they decay, to do so in one way of ...
0
votes
1answer
95 views

Is kinetic energy in QM a state-property or is it distributed?

Suppose we have a quantum mechanical system, which is well described by its wave function in r-representation $\Psi$. We are interested in the properties of an observable, say the kinetic energy $T$. ...
1
vote
0answers
26 views

Troubles with the Nucleon Bound Energies

I was reading my quantum mechanics text and I have a doubt. I have the energy levels well defined for the finite square well and the author suddenly compares (I believe) those levels with the levels ...
4
votes
1answer
147 views

Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$ V_{0}(r) = -\frac{Z}{r} $$ into $$ V(r) = -\frac{g}{r^{\frac{3}{2}}} $$ with $g$ a positive ...
1
vote
1answer
152 views

Energy and time evolution of a particle in a potential well

Hoping this is not a silly and stupid question let me ask for help in this problem. I have a particle in an infinite square well (the box is from 0 to a), in the state described by the function ...
0
votes
0answers
40 views

Which is more energy efficient: optical demagnetization or heating beyond $T_c$,

What is considered more energy efficient? Current research show that the amount of energy used for powering a laser to demagnetize a material is quite small. However, the demagnetization is very ...
0
votes
1answer
144 views

Integers, Energy levels, and wavenumbers for a particle in a 2D box

(This question is not about coding) I have built a little code in Python that allows the user to plot the energy vs the wave number of particle in a 2D box, depending on what values for the integers ...
0
votes
5answers
324 views

Do electrons collapse into nucleus, if electrons in the atom are constantly excited?

From the Bohr's atomic model, it is clear that electron can have only certain definite energy levels. When the electron is present as close to the nucleus as possible, the atom has the minimum ...
8
votes
1answer
112 views

Does quantum collapse involve a loss of information? Does it require energy as suggested by the Landauer Limit?

I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called ...
2
votes
1answer
119 views

Estimating minimum energy with uncertainty principle

I'm currently trying to solve a problem that involves estimating the minimum energy of a particle in the potential: $$ V(x) = \frac{-V_0a}{|{x}|} $$ I'm quite confused about how to handle the ...
0
votes
0answers
22 views

Calculating the stability/invertibility of energy maps by multivariate time series model

You have the following energy maps for 14 different structures so about 4-5 pixels for one unit. The color density represents energy. I am thinking that you can set multivariate time series models ...
0
votes
2answers
146 views

Do any other particles get excited(or absorb energy) by photons like electrons?

Electrons get excited to different energy levels when photons of specific frequencies fall on them.But, is there other particles which absorb the energy of the photons?
0
votes
1answer
253 views

How to derive or justify the expressions of momentum operator and energy operator?

It has been noted here$\! { \, }^{\text(1, 2)}$, for instance, that $$\mathbf{F} = \frac{d}{dt}\!\!\biggl[ \, \mathbf{p} \, \biggr]$$ is true in all contexts. Likewise, in notable contexts it is ...
0
votes
0answers
45 views

Energy required to demagnetize a soft iron?

How much energy is required to demagnetize a soft iron ferromagnetic material, that has a very low coercive force And a small hysteresis area? Also, would it be possible to demagnetize that same ...
0
votes
1answer
151 views

Hamiltonian operator apply to a wavefunction

When a Hamiltonian operator apply to a wavefunction, how could we write the hamiltonian as, $$H \psi = (E_n-\hbar \omega_0) \psi \ \ ? $$ Is this because $E_n= H+ \hbar \omega_0$? where ...
1
vote
1answer
74 views

Wave Function of Particle in Nuclear Reaction

I was thinking and came up with the question of what happens to the wave function of a particle that decays into energy, say a neutron in a nuclear reaction. I know that conservation of probability ...
0
votes
0answers
158 views

attractive and repusive potential barrier

In the paper of quantum mechanics we have a topic "attractive and repulsive potential barriers" included alongwith the potential step problem.I wonder what does attractive and repulsive potential ...
0
votes
3answers
555 views

Simple harmonic oscillator: zero point energy?

Today we had a lecture on the simple harmonic oscillator and its quantum mechanical treatment. My teacher derived the equation for it and finally concluded it has some zero point energy. My ...
1
vote
3answers
297 views

What is the energy of a standing EM wave? Is it probabilistic?

In a cavity, the standing wave will constructively interfere with itself, so its energy gets higher while the oscillator is still vibrating. Since the vibration time is not a constant value, and ...
6
votes
2answers
302 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where ...
0
votes
0answers
23 views

What are physical effects that could be employed to emulate this system?

This is a simple system consisting of a tree of numbers such as ((1 2 (3 4)) (2 6) 1 6) and a rule of application, that states that a tree A applied to B is a copy ...
1
vote
2answers
991 views

The Energy Eigenvalue of a Wavefunction

I've been reading an introduction to quantum mechanics online, and while constructing the Schrodinger equation for a free particle, the equation $i\hbar \frac{d \Psi}{dt}=\hbar\omega\Psi$ is obtained. ...
6
votes
3answers
466 views

Connection between $\Delta x \Delta p \geq \frac{\hbar}{2}$ and $\Delta E \Delta t \geq \frac{\hbar}{2}$

Is there a way to derive second equation from the first one? I mean is there a connection between those two uncertainty relations? \begin{align} \Delta x \Delta p &\geq \frac{\hbar}{2}\\ \Delta ...
3
votes
1answer
157 views

Energy of an EM wave compared to energy of a photon

Several posts on this forum ask the question about the role of amplitude in calculating the energy of an Em wave. This struck me as odd since I learned that E=hv. There is no amplitude in the Planck ...
5
votes
2answers
202 views

Energy time complementarity from unitary evolution

I am looking for a well posed experimental situation that illustrates energy time complementarity. I know of Einsteins box, which is discussed quite nicely in Bohr's article Discussions with Einstein ...
-2
votes
1answer
107 views

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 ...
5
votes
1answer
368 views

Do electrons need specific energies to excite electrons

Photons need specific energy levels, equal to the difference between two energy levels to excite an electron in an atom. Is this the same case with electrons that collide with atoms?
1
vote
1answer
224 views

Definition of energy

What is the definition of energy $E$ given a dispersion relation $\omega=\omega(k)$ where $k=|\vec k|$ and $\omega$ is not necessarily linearly proportional to $k$? What about momentum $\vec p$? This ...
2
votes
1answer
147 views

How is energy transferred between atoms in a collision?

Consider two bare protons. One (A) is stationary (relative to some arbitrary massless observer); the other (B) is approaching A at 1 m/s. When they collide, I assume that they bounce. What is the ...
16
votes
3answers
3k views

Amplitude of an electromagnetic wave containing a single photon

Given a light pulse in vacuum containing a single photon with an energy $E=h\nu$, what is the peak value of the electric / magnetic field?
2
votes
2answers
2k views

Two expressions for expectation value of energy

I was looking up expectation value of energy for a free particle on the following webpage: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/expect.html It says that $E=\frac{p^2}{2m}$ and ...
8
votes
4answers
892 views

What matter in the original atom bomb is converted to energy?

When an atom bomb goes off some matter is converted to energy according to $E = m c^2$. I'd like to know exactly what matter in the original atom bomb is converted to energy. Is it protons, neutrons, ...
1
vote
2answers
1k views

Conservation of Energy in a magnet

When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply ...
2
votes
1answer
186 views

Why don't cancelling wavefunctions for two different particles give zero total wavefunction?

Let $\left|a\right>=e^{i(kx-\omega t)}$, $\left|b\right>=-e^{i(kx-\omega t)}$ be two neutral particles in the 1D free space without any interaction. Then ...
2
votes
2answers
99 views

Is there any correlation between the energy density fluctuations of two separate systems in a vacuum state?

I think the title says it all. What I am curious to find out is if there are any observable changes in the fluctuations of zero-point energy in a vacuum state system that are the consequence of ...
-1
votes
2answers
175 views

Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
0
votes
2answers
321 views

Momentum Energy and Higgs

So, as an object accelerates it gains energy. And energy is mass. So an object becomes more massive as it approaches the speed of light. But, if mass is ONLY due to an object's interaction with the ...
1
vote
2answers
319 views

Einstein's Mass-Energy Equivalence versus Quantum Kinetic Energy

Using a naive view of Einstein's Energy Mass Equivalence $E=mc^2$ (where m is mass and c is the speed of light), it seems tempting to interpret this as a quantum mechanical version of the inherent ...
1
vote
1answer
105 views

Is the Energy Sharply or Fuzzily Defined in Quantum Mechanics?

According to quantum mechanics, energy of a state is uncertain within a small range in hydrogen atom. But we also know that energy of a state is quantized which is contradictory to the first. Which ...
12
votes
4answers
819 views

Energy is actually the momentum in the direction of time?

By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong?
4
votes
2answers
132 views

Do asymptotically similar potentials yield similar energy levels asymptotically?

Let there be given two Hamiltonians $$H_1~=~ p^{2}+f(x) \qquad \mathrm{and} \qquad H_2~=~ p^{2}+g(x). $$ Let's suppose that for big big $x$, the potentials are asymptotically similar in the sense ...
5
votes
2answers
660 views

Energy operator

Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...