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56 views

Does the second-order correction to degenerate perturbation theory vanish?

Consider a degenerate two-state system with states denoted by $|1\rangle$ and $|2\rangle$. If we apply a perturbation $H^\prime$, the first order correction to the energy is obtained by choosing two ...
31
votes
4answers
4k views

Why does the Schrödinger equation work so well for the hydrogen atom despite the relativistic boundary at the nucleus?

I have been taught that the boundary conditions are just as important as the differential equation itself when solving real, physical problems. When the Schrödinger equation is applied to the ...
2
votes
1answer
58 views

What is wavelength at classical turning points using WKB Approximation? [closed]

According to what I know is that a classical turning point in Newtonian Mechanics is a point where a particle has a zero kinetic energy (Total energy is equal to potential energy) and must be ...
0
votes
0answers
31 views

What happens to renormalisation counter-terms in the classical limit?

My understanding is we add counter-terms to the actions in the process of renormalisation. Presumably these terms don't have a physical effect in a classical interpretation of the action. i.e. they ...
3
votes
2answers
148 views

Is it possible to have mass with zero volume?

As we had always studied that matter occupied space and has mass and our universe is made of matter so do that mean that there is no case where mass is present without volume .
-3
votes
1answer
58 views

Has quantum mechanics been able to define the centre of a black hole? [closed]

It is said that quantum mechanics has defined everything we observed everything so far, but did it predict the existence of the Higgs Boson beforehand and has it been able to define the Singularity?
0
votes
1answer
190 views

Black hole maximum mass/stress-energy limit?

I have read these questions: Why does a black hole have a finite mass? Are black holes an infinite source of energy? Black Hole: mass density or energy density? Do all black holes have the same ...
5
votes
1answer
276 views

What is the quotient of two quantum operators?

It's probably useful to explain the context, which led me to this question. We were asked the following question: By writing ${L}^2 = \sum_{ijklm}\epsilon_{ijk}{x}_j{p}_k\epsilon_{ilm}{x}_l{p}_m$ ...
0
votes
1answer
29 views

Semiclassical propagator convergence at $t=0$

For harmonic oscillators the prefactor for the semiclassical propagator is $Fe^{iS}$ where $$F=\sqrt {m\omega/{2πi\hbar\sin(ωt)}}$$ and $$S={m\omega[(x_0^2+x_1^2)\cos(\omega t)-2x_0x_1]}/{2\sin(\omega ...
2
votes
1answer
321 views

Is this expression for radial probability flux in Sakurai's Modern Quantum Mechanics wrong?

The section on Schrodinger's equation for central potentials in Sakurai's Modern Quantum Mechanics (p. 208, 2nd edition) contains the following expression for the radial probability flux, as part of ...
5
votes
2answers
574 views

Why are S-state solutions of Dirac equation for hydrogen atom allowed to be unbounded?

In this Wikipedia page there's a statement about 1S orbital as solved from Dirac equation: Note that $\gamma$ is a little less than $1$, so the top function is similar to an exponentially ...
4
votes
3answers
356 views

Is the energy really infinitely large in a measurement of the energy immediately after the measurement of the position?

For instance, assume the particle rests on the ground state $\psi_0 (x)$ of a one-dimensional simply harmonic oscillator around the origin of axes $ x=0 $, and once we measure the position of the ...
11
votes
3answers
717 views

Are there any true discontinuities in physics?

When we first learn physics, it's often presented very 'discontinuously'. For example, pop quantum likes to talk about objects being "either" particles or waves, leading to a lot of confused questions ...
0
votes
0answers
80 views

Is it almost impossible to separate two point charges stuck together?

$$F=k\frac{qQ}{r^2},$$ if $r\rightarrow 0$ then $F\rightarrow \infty$.
6
votes
2answers
323 views

Is Quantum Coulomb still singular?

A single free charge (e.g. electron) $q$ fixed at the coordinate origin has the well-known Coulomb/electric potential $$\phi(\vec r) = \frac q{4\pi\epsilon_0}\frac 1r \tag{A}$$ where $r=|\vec r|$ of ...
7
votes
1answer
1k views

Am I missing a trick to solving a 3D potential well problem?

I was playing around with a 3-D potential $V$ such that $V_{(r)} = 0$ for $r<a$, and $V_{(r)} = V_0>0$ otherwise. By using the Schrödinger Equation, I showed that: $$\frac{-\hbar}{2m}\frac{1}{r^...
6
votes
1answer
198 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
8
votes
4answers
783 views

An electron falling into a black hole

If an electron falls into a black hole. How can the Heisenberg uncertainty principle hold? The electron has fallen into the singularity now so it has a well defined position which means that it doesn'...
6
votes
2answers
2k views

Radial Schrodinger equation with inverse power law potential

Recently I read a paper about solving radial Schrodinger equation with inverse power law potential. Consider the radial Schrodinger equation(simply set $\mu=\hbar=1$): $$\left(-\frac{1}{2}\Delta+V(\...