## Why is it important that Hamilton’s equations have the four symplectic properties and what do they mean?

The symplectic properties are: time invariance conservation of energy the element of phase space volume is invariant to coordinate transformations the volume the phase space element is invariant with respect to time I’m most inerested in what 3 and 4 mean and why they are important. Answer Coordinate invariance guarantees that the phase space M … Read more

## Is an electron/proton gun possible?

In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of the “cathode”. … Read more

## Light and parabola

I know that parallel light beams hitting a parabola will be focused at the focus of the parabola (f = 1/4a) and a light source at the focus of the parabola will produce parallel light. What will happen if the light was not parallel but came from a light source shorter then the focus of … Read more

## What is the relationship between AC frequency, volts, amps and watts?

In an alternating current, how are frequency, voltage, amperage, and watts related? For instance, imagining the power as a sine wave, what is amperage if voltage is the amplitude? Is there a better analogy than a sine wave? EDIT: One of the things I specifically wanted to know is whether frequency and voltage are related? … Read more

## What are some interesting calculus of variation problems? [closed]

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## Alternative definitions of potential?

I hope this question is simple and can be quickly cleared up. In a 1D conservative dynamical system, I’ve always been taught that the potential function is the function V(x) such that: F=−dVdx That makes sense to me, simply derived from the definitions of work and conservation of energy. However, just reading through the book … Read more

## Uniqueness of eigenvector representation in a complete set of compatible observables

Sakurai states that if we have a complete, maximal set of compatible observables, say A,B,C… Then, an eigenvector represented by |a,b,c….>, where a,b,c… are respective eigenvalues, is unique. Why is it so? Why can’t there be two eigenvectors with same eigenvalues for each observable? Does maximality of the set has some role to play in … Read more

## Quantum harmonic oscillator

I read somewhere that a quantum field can be thought of as a tiny bowl at every point in space with a ball doing SHM (quantum harmonic oscillator). It was given that the amplitude of this SHM is quantized, and each quantum signifies a particle. (i.e. if the ball rolls with minimum amplitude, there are … Read more

## Entanglement and the double slit experiment

Is the double slit experiment an example of entanglement when it seems as if the photon is going through both slits? Or put another way, is it at this stage when we attempt measurement we see a photon on one side affect the photon on the other side? Do entangled particles have to be made … Read more

## How to apply an algebraic operator expression to a ket found in Dirac’s QM book?

I’ve been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac’s book. In the fourth edition, 33rd page, starting from this:ξ|ξ′⟩=ξ′|ξ′⟩ (Where ξ is a linear operator and all the other ξ′‘s are eigen-(value|ket)s.) ,and this:ϕ(ξ)=a1ξn+a2ξn−1⋯an=0 (where ϕ is an algebraic expression) He has deduced ϕ(ξ)|ξ′⟩=ϕ(ξ′)|ξ′⟩ I understand … Read more