Tagged Questions

2
votes
1answer
103 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
2
votes
0answers
31 views

When is classical mechanics valid for describing motion of atoms?

In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength ...
12
votes
1answer
230 views

Classical results proved using quantum mechanics

Are there any results in classical mechanics that are easier to show by deriving a corresponding result in quantum mechanics and then taking the limit as $\hbar\rightarrow0$? (Are there classical ...
1
vote
3answers
174 views

Is a quantum system mandatory for generating true random sequence?

Is a quantum system necessary if we want to generate true random sequence? The mathematical framework used for classical mechanics doesn't involve any random value. But the mathematical framework of ...
6
votes
3answers
342 views

When does $\hbar \rightarrow 0$ provide a valid transition from quantum to classcial mechanics? When and why does it fail?

Lets look at the transition amplitude $U(x_{b},x_{a})$ for a free particle between two points $x_{a}$ and $x_{b}$ in the Feynman path integral formulation $U(x_{b},x_{a}) = \int_{x_{a}}^{x_{b}} ...
3
votes
3answers
189 views

Are quantum mechanics and determinism actually irreconcilable? [closed]

As a preface, I am not a physicist. I'm simply interested in abstract physics and fundamental principles of the universe and such. As such, if you can provide an answer for the layman (as ...
3
votes
1answer
395 views

Differences of behaviour of a particle in a box in quantum theory between that in classic physics

Can anyone help me enlist 3 major differences between the quantum and classical physics of the behaviour of a particle in a box? I would like some insight into the differences without solving PDEs ...
0
votes
2answers
78 views

Quantum Conservation versus classical conservation

If energy is conserved in all quantum mechanical interactions, how are there classical interactions in which energy is not conserved, given that classical interactions are a macroscopic approximation ...
7
votes
3answers
308 views

Force through quantum mechanics

In classical physics force is: $$F=\frac {dp}{dt}$$ How about quantum mechanics? In Old Quantum Mechanics momentum is: $p=\hbar \cdot k$ so force will be: $$F=\hbar \frac {dk}{dt}$$ what does $\frac ...
15
votes
11answers
974 views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
1
vote
1answer
141 views

Problem in Hamiltonian

I need to elaborate the equation ,and need to know what is the physical significance and how matrices will manipulate in the equation $$ \hat{H} = (\hat{\tau_3}+i\hat{\tau_2})\frac{\hat{p}^2}{2m_0}+ ...
2
votes
0answers
93 views

Eternal clocks and 4D spacetime crystals

There was a recent article about the creation of 4D spacetime crystals based on recent theory proposed by Frank Wilczek. This theory is based on breaking time translational symmetry which basically ...
4
votes
1answer
168 views

Quantum $n$-body problem

Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential ...
2
votes
2answers
382 views

What the difference between “orbital” and “orbit”?

What's the difference between "ortibal" and "orbit"? Which one should be used in physics? In quantum mechanics, is "atomic orbital" or "atomic orbit" used? And what about in classical mechanics? A ...
7
votes
8answers
483 views

Is “Causality” the equivalent of a claim that the future is predictable based on the present and the past?

In classical (Newtonian) mechanics, every observer had the same past and the same future and if you had perfect knowledge about the current state of all particles in the universe, you could ...
2
votes
1answer
196 views

Euler angle: space-fixed vs body-fixed axes

I am sooo confused!! Between active and passive, intrinsic and extrinsic, vectors and basis .... Stipulate that we stick to active rotations only. Then Standard derivation of $R(\alpha, ...
3
votes
2answers
191 views

Classical Limit of Commutator

In Dirac's book on quantum mechanics (4th ed., pgs 87-88), he seems to give a very elementary argument as to how the commutator [X,P] reduces to the Poisson brackets {x,p} in the limit h_bar->0. ...
5
votes
4answers
535 views

Classical Limit of Schrodinger Equation

There is a well-known argument that if we write the wavefunction as $\psi = A \exp(iS/\hbar)$, where $A$ and $S$ are real, and substitute this into the Schrodinger equation and take the limit $h \to ...
3
votes
2answers
457 views

Classical Limit of the Feynman Path Integral

I understand that in the limit that h_bar goes to zero, the Feynman path integral is dominated by the classical path, and then using the stationary phase approximation we can derive an approximation ...
4
votes
5answers
471 views

Classical limit of quantum mechanics

I have heard that one can recover classical mechanics from quantum mechanics in the limit the $\hbar$ goes to zero. How can this be done? (Ideally, I would love to see something like: as $\hbar$ ...
2
votes
1answer
237 views

Classical limit of the path integral formulation of quantum mechanics

It is well-known that if $S \gg \hbar$, then the classical path dominates the Feynman path integral. But is there some to show that if $S\gg\hbar$, then the particle's trajectory will approach the ...
5
votes
3answers
444 views

How does one quantize the phase-space semiclassically?

Often, when people give talks about semiclassical theories they are very shady about how quantization actually works. Usually they start with talking about a partition of $\hbar$-cells then end up ...
1
vote
0answers
20 views

On Bolte's semiclassical law

i have seen on internet the following, for $ E >> 1 $ the Eigenvalue Staircase can be approximated by $ N(E)= \frac{1}{\pi}argZ(1/2+i \sqrt E ) $ ...
9
votes
2answers
275 views

When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
7
votes
3answers
294 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
3
votes
2answers
354 views

Connections between classical and quantum mechanics?

I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere ...
5
votes
3answers
214 views

What is the Quantum equivalent of chaos on a classical system? (if there's any)

This is a question that bugging me around for some time now. It is not clear to me what is the meaning of a chaos if we consider a quantum system. What is the mathematical formalism (or the quantum ...
7
votes
6answers
318 views

How does such strange microscopic behavior at the atomic level (quantum mechanics) lead to the macroscopic behavior at our level?

So, I'm only a high school student researching quantum physics, and I find it very interesting. However, there's one question that keeps nagging at me in the back of my head. How exactly do odd ...
5
votes
3answers
313 views

Some questions on observables in QM

1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable? 2-What are the criteria to say whether ...
0
votes
2answers
140 views

Are all classically impossible quantum possibilities entangled?

Any entangled state represents a quantum possibility that is classically impossible. Is the converse true? That is, are all states that are quantum mechanically possible but classically impossible ...
1
vote
1answer
373 views

Conjugate Variables and Fourier Transforms in Classical Physics

Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be ...
8
votes
5answers
493 views

Is it possible to recover Classical Mechanics from Schrödinger's equation?

Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
4
votes
2answers
457 views

Canonical momentum in different coordinate system

The canonical momentum is defined as $p_{i} = \frac {\partial L}{\partial \dot{q_{i}}} $, where $L$ is the Lagrangian. So actually how does $p_{i}$ transform in one coordinate system $\textbf{q}$ to ...
1
vote
0answers
80 views

Giving some intuition of particle physics, quantum physics,classical mechanics etc etc to a layman [closed]

I am a software engineer by profession and sometimes get curious on some physics terms I hear about and expect myself to have some at least basic intuition of what it is all about. I keep hearing of ...
9
votes
2answers
348 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
2
votes
1answer
190 views

Church–Turing Thesis

Can the Church–Turing Thesis be proved assuming classical mechanics, how is the proof or disproof? Edited: I was looking for a proof of "everything computable by a device obeying CM is computable by ...
3
votes
3answers
150 views

Are there measurable effects to scaling the action by a constant?

Classically, we obtain the equations of motion by finding a path which has an action that is stationary with respect to small changes in the path. That is the path for which: $\delta S =0$ Scaling ...
5
votes
3answers
609 views

Why is tunneling not a classical idea?

There is no tunneling in the case of infinite potential barrier, but there is when we have a finite well. In the classical analog, in the first case we have a particle bouncing between to infinitely ...
3
votes
4answers
488 views

Radiation from a pair of charged objects orbiting each other

This question on binary black hole solutions, led to me think about the similar question from the perspective of what we know about the Hydrogen atom. Prior to quantum mechanics, it was not ...
-4
votes
2answers
2k views

What are the main differences between these quantum theories?

What are the main differences between these quantum theories? Quantum Mechanics Quantum Field theory Quantum Gravity EDIT: I ask this question because when I asked a question before people talk ...
2
votes
3answers
428 views

Why is it hopeless to view differential geometry as the limit of a discrete geometry?

This is a follow-up question to Introductions to discrete space-time: Why is this line of thought hopeless? Classical mechanics can be understood as the limit of relativistic mechanics $RM_c$ ...
37
votes
9answers
3k views

Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...