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34 views

Stationary State of Quantum Mechanics [duplicate]

Why for every normalized solution to the time-independent Schrödinger equation $E$ must exceed the minimum value of $V(x)$?
2
votes
1answer
68 views

Differing definitions of Gibbs free energy and Helmholtz free energy

I am trying to understand, to me, the difficult concepts of thermodynamic potentials, and I find their definitions numerous and hard to connect between each other. For instance, here are two ...
3
votes
2answers
167 views

Energy measurement from position eigenstate

Given that the eigenstates of the position operator can be written as $\delta(x-x')$, and suppose we measure a particle in an infinite potential with walls at $x=0$ and $x=L$. I measure the particle ...
2
votes
1answer
116 views

Energy formula for finite potential well [closed]

The energy formula for infinite potential well is $$E=\frac{n^2h^2}{8ma^2},$$where $m$ is the mass of the particle, $a$ is the width of the well but in the case of finite potential well, I actually ...
0
votes
4answers
249 views

Electron in free space and Schrodinger's equation

Topic: Quantum Theory of Solids I have come across the following text: Electron in Free Space: Consider the motion of an electron in free space. If there is no force acting on the particle, ...
2
votes
4answers
147 views

Does a particle with infinite energy escape an infinite well?

Currently, my modern physics class is going over particles in finite and infinite wells, general quantum formalism, and tunneling. What happens to a particle as it gains an infinite amount of energy? ...
0
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0answers
64 views

Taylor expansion for a double well/perturbed infinite square well

I'm trying to estimate the ground state energy for a perturbed infinite square well directly. The potential is piecewise constant $$V(x)=\begin{cases}&\infty, \qquad x<-a/2\\ &0 \qquad -a/2&...
0
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1answer
23 views

Interactions between “particles” to prevent diffusion and to cause phase segregation

The free energy of particles reads, if we assume no internal energy : $\tilde f(c)= \frac{f(c)}{k_bT}=-c \, ln(c)-(1-c)\, ln(1-c)$, with $c$ the concentration. If we had a term $F(c)$ for the ...
5
votes
2answers
327 views

Physical Significance of $U$ (Internal Energy ) , $H$ (Enthalpy) , $F$ (Free Energy) and $G$ (Gibbs Free Energy)? [closed]

I know their mathematical definitions and how these terms are interrelated (mathematically) but I fail to understand the physical meaning of none but one which is INTERNAL ENERGY . It seems ...
0
votes
1answer
30 views

What's Gravitational Potential Energy of a Balanced Mass on a single Point?

Anyone know how to calculate the gravitational potential energy of a balanced Mass such as an upside down 2d triangle balanced on a single point. Is there any way to calculate the gravitational ...
-1
votes
1answer
64 views

What is happening energy-wise when an object is suspended on rope from ceiling?

Several similar questions have been asked, e.g. this one, but all of them used the example of muscle work, so it was clear where the energy went. However, suppose we suspend an object on a rope from ...
1
vote
1answer
427 views

Energy loss in Fluid flow

In a constant diameter, ground level pipe of substantial length to reflect a pressure drop of dP, how would the loss of energy be accounted for? The assumption would be that kinetic and potential ...
-1
votes
1answer
41 views

How can negative total energy mean a bound state is potential zero is arbitrary?

My Understanding is that if the Hamiltonian (H) plus potential (V) of a particle if negative than we have a bound state. However I also know that a potential is defined by placing a zero at an ...
0
votes
1answer
56 views

Question about creating a High energy gap

I'm studying junior physics where I learned the particle in a box and also Bohr's atom. Where the energy gape was give by $\Delta E_{n+1\rightarrow n}=((n+1)^2-n^2)E_1$ and $\Delta E_{n+1\...
2
votes
1answer
44 views

Is there an easy way to know on which variables a thermodynamic potential depends?

I have no problem identifying the variables if the differential form of a potential is given, for example, $$ dU = T\,dS - P\,dV + \sum_i \mu_i\, dN_i $$ $U$ is then (like $dU$) a function of $$S, V, ...
0
votes
2answers
51 views

Concerning the type of energy carried by electrons in a circuit

See for example this circuit The resistor shown has a "potential difference" of 10V across it. Now we know that this refers to the work done per unit charge... The change in energy per unit charge. ...
2
votes
1answer
49 views

Dependence of energy $E$ with principal quantum number $n$

Is there any way to tell how the energy levels of a potential well depend upon the quantum number $n$, looking at the potential, before solving? I mean, for harmonic oscillator, $E\sim n$, for ...
0
votes
1answer
78 views

In what field is the particle $L=\frac{m}{2}\eta_{\mu\nu}u^{\nu}u^{\mu}+\frac{k\,x^3\,u^0}{((x^1)^2+(x^2)^2+(x^3)^2)^2}$

The following Lagrangian describes the behavior of a charged particle placed in a field. $$L=\frac{m}{2}\eta_{\mu\nu}u^{\nu}u^{\mu}+\frac{k\,x^3\,u^0}{((x^1)^2+(x^2)^2+(x^3)^2)^2}$$ It is a ...
0
votes
1answer
105 views

How can I calculate the force a giant knife applies to a car if it cuts straight through?

I feel like this is a really basic question but I'm struggling to come up with a straightforward answer! In this video: https://youtu.be/wdCt3pjtgAA?t=49 We see a 10 foot knife dropped from 30 ...
1
vote
1answer
52 views

Will dipole be restored to its Initial position after removing uniform electric field from it?

Potential Energy is the amount of energy which gets stored in the system when external Force is applied on the system. And the system can give us back that energy in any energy form. Keeping above in ...
4
votes
2answers
185 views

Misconception about electrostatic energy

The electrostatic energy of a charge distribution $\rho$ is \begin{equation} U=\int\rho(\vec{r})\ \phi(\vec{r}) \ dV \end{equation} where $\phi$ is the electric potential generated by the charge ...
1
vote
1answer
72 views

How have we derived the definition of gravitational potential energy? [duplicate]

The gravitational potential energy of an object at a point above the ground is defined as the work done is raising it from the ground to that point against the gravity. How has this definition been ...
0
votes
1answer
145 views

Bound states for the Delta Function Well

In "Introduction to Quantum Mechanics" by Griffiths we discussed the delta potential well. They speak about bound and scattering states for $E<0$ and $E>0$ resp. But before that (Problem 2.2) we ...
-1
votes
1answer
3k views

Work done by force moving a pendulum

So there's this problem I can't understand where I need to calculate the work done by force F to move the pendulum at a constant speed from one point to the other. The correct answer is mgL(1 - cos(θ))...
0
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2answers
99 views

Potential energy in NMR and energy level transition

I am slightly confused about the fact that when we are considering, for example, magnetic resonance or electron transition between energy levels, we seemed to only consider the potential energy in ...
0
votes
2answers
134 views

Find electrostatic energy - Is there a typo? [closed]

The problem asks me "Show that the electrostatic energy $U$ of a charge $q$, subject to an electric potential $\Phi(\boldsymbol r)$ is $U = q \Phi(\boldsymbol r)$ My trial The electrostatic energy ...
0
votes
2answers
379 views

Gravitational Potential Energy and Zero Points

I have two questions. 1) The first one has to do with the formula for deriving Gravitational Potential Energy. I learned that, for the derivation of Gravitational Potential Energy given large ...
0
votes
1answer
294 views

Internal energy and rest mass energy

when a cup of water is at rest, does the potential energy between water molecules contribute to the rest mass or just the kinetic energy of the molecules? Also, is it the same as asking whether the ...
0
votes
0answers
58 views

Why is the potential electrical energy defined as the negative of the work integral, using couloumbs law to represent the force?

I saw many questions formulated more or less with the same words, but what I am not understanding here is different. The Coulomb law describe a force in a charge by others charges in the environment, ...
3
votes
1answer
43 views

Predicting the value of $n$ for the energy of a wavefunction in the infinite square well by inspection

$$E=\frac{n^2 \pi ^2 \hbar^2}{2ma^2}$$ Is it always possible to tell the value of $n$ by inspecting the shape of the wavefunction in the infinite square well no matter what the value of $a$ is? ...
3
votes
2answers
6k views

Two conducting spheres connected by a wire

There are two conducting spheres of different charge and a conducting wire. After they are connected by the wire, charge flows between the spheres. The charge distributes itself so that the spheres ...
1
vote
1answer
130 views

charged plasma and ion grid in interaction in ion thrusters

I was just wondering ..... In this Image of an ion thruster, when the positively charged particles pass through the grids, wouldn't they just bombard the negatively charged grid(a fraction of them). ...
1
vote
0answers
59 views

How much electric energy is created by an 80kg man making a step at flat surface while walking at the normal speed (5km/h) [closed]

Even a rough approximation would be helpful. But of course a precise calculation would be great :). Thank you all in advance very much for your help! By the way - do you have any suggestion for ...
0
votes
1answer
77 views

Particle incident on a potential barrier

Given a step potential $V_0$ at $x=0$ (potential is zero to the left of the origin and $V_0$ to the right towards infinity) and a particle approaches it from the left with energy $E=2V_0$. I solved ...
1
vote
1answer
838 views

Energy functional - potential energy?

Consider $$ u_t=u_{xx}+f(u), x\in\mathbb{R}. $$ We can write $$ u_t=\nabla_{L^2}E(u) $$ for the energy functional $$ E(u):=\int_{\mathbb{R}}\frac{1}{2}u_x^2+F(u)\, dx, F(s):=\int_0^s f(s). $$ Here, $\...
-1
votes
1answer
56 views

density and inertial mass

Water's density at 60-degree Fahrenheit is 62.366 pounds/ft^3. Is it inertial or gravitational mass? Actually, I am trying to calculate Potential Energy (PE) of 1 gallon of water at 1' height. Is PE = ...
0
votes
0answers
132 views

Calculating workout energy burned per rep

I received this machine as a gift. Now, the name is a bit ridiculous and implies I only need to use it 5 minutes per day in order to slim. From a physics perspective that doesn't make any sense. In ...
0
votes
1answer
17k views

How to calculate KE using only mass and height [closed]

For our physics (high school level) group project, we were asked to modify a selected toy so that it produces an energy output of at least or roughly 110% (10% more) compared to the original toy. Our ...
0
votes
1answer
43 views

Could the force accelerating a particle be derived as the gradient of the spatial distribution of kinetic energy?

If a point mass is accelerated by a force $\vec{F} = m \vec{a}$ the kinetic energy $T$ could be derived from $$T = \int_{\vec{r_0}}^{\vec{r}}{\vec{F} \cdot d\vec{r}} = \int_{\vec{r_0}}^{\vec{r}}{m \...
2
votes
1answer
667 views

Degeneracy of energy levels of a particle in a spherical step potential in 3D?

I have a particle of mass $m$ and spin $1/2$, in a spherical step potential, $$ V(r) = \begin{cases} 0 & r<a, \\ V_0>0 & r>a. \end{cases} $$ Now they ask me to find, without solving ...
14
votes
4answers
924 views

Increasing a potential causes increase in energy levels

Suppose a potential $V(x)$, and suppose a bound particle so the allowed energy levels are discrete. Suppose a second potential $\widetilde{V}(x)$ such that $\widetilde{V}(x) \geq V(x)$ for all $x$ (...
0
votes
1answer
545 views

Do energy levels such as $E_c$, $E_v$ have negative values in semiconductors?

In energy band diagram of a semiconductor, do energy levels such as $E_c$, $E_v$ have negative values? Also, why electrons in semiconductor have energy? What is the formula for energy of an ...
3
votes
1answer
113 views

Why is the energy shift due to a 'sagging' potential negative and independent of box size?

Consider a box of width $L$ and the composed of the following potential $$V(x)=\frac{V_0x(x-L)}{L^2}, x\in[0,L]$$ and $V(x)=\infty$ elsewhere. Using perturbation theory - with a square box as the ...
0
votes
1answer
28 views

Since a dipole has some potential energy,it should be able to do some work !? What is it?

We say a dipole has potential energy.What work can a dipole do ?.For eg : A ball on a shelf has a PE because it has the potential to fall down and do some work on the ground if shelf wasnt there.What ...
-1
votes
1answer
93 views

Particle in infinite square well with $\langle E \rangle = (1/4) E_1 + (3/4) E_4$

Suppose we have a particle in an infinite square well with $\langle E \rangle = (1/4) E_1 + (3/4) E_4$. I know that I can calculate the uncertainty in the particle's position by $\sqrt{\langle E^2 \...
1
vote
1answer
3k views

Does the kinetic energy change depending on the direction of the velocity? [closed]

The kinetic energy is calculated with the following formula: $$E_k = \frac 12 mv^2$$ Does $v$ represent the value of the velocity? I mean, if you have a specific direction of the velocity is the ...
1
vote
1answer
3k views

Calculating potential energy per ion of an one dimensional ionic crystal

The problem states to calculate "the potential energy, per ion, for an infinite 1D ionic crystal with separation $a$"; the crystal is a 1D lattice of alternating charges, likes so: $$...+-+-+-+-+-...$...
0
votes
1answer
34 views

Basic PE question about moving a planet.

If you lifted enormous masses (eg. many gigantic rocks) at one point (A) of the planet's equator. Then after 180 degree planet rotation, released the potential energy by lowering the rocks (B). (*...
0
votes
2answers
3k views

Mass hanging from spring: potential energy [closed]

I have encountered a problem with a mass $m$ hanging from a spring. I want to find the maximum distance it will be stretched from the spring's equilibrium. At the maximum distance the spring is ...
-1
votes
1answer
175 views

Zero Energy State of a Mechanical System? [closed]

Would a mechanical system in a particular frame (when I say mechanical I mean pulleys, elastic strings, etc.) that has no potential energy (loaded springs, pulled back elastic, hanging weights, etc.) ...