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### Stationary State of Quantum Mechanics [duplicate]

Why for every normalized solution to the time-independent Schrödinger equation $E$ must exceed the minimum value of $V(x)$?
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 ...
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 ...
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 ...
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, ...
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? ...
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### 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. ...
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 ...
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 ...
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 ...
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 ...
185 views

The electrostatic energy of a charge distribution $\rho$ is $$U=\int\rho(\vec{r})\ \phi(\vec{r}) \ dV$$ where $\phi$ is the electric potential generated by the charge ...
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### 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 ...
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 ...
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))...
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### 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 ...
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 ...
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 ...
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 ...
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, ...
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### 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? ...
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 ...
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). ...
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 ...
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 ...
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### 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). (*...
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 ...