Quantum-mechanics Definition and 14 Threads

Suppose I have 100 identical boxes of length L and the coordinates are x=0 at one end of the box and x=L at the other end, for each of them. Each has a particle of mass m. V=0 in [0,L], while it's equal to infinity in the rest of the regions. If I make a measurement on position of the particle...

Summary: Questions about the Multiverse hypothesis and the 'No boundary' conditions approach in cosmology I have some questions about James Hartle and Stephen Hawking's 'No-boundary' proposal: - In their approach multiple histories would exist. These histories could yield universes with...

Does anyone know the answers to this, or can hopefully guide me to a text that will help me solve this aharonov-bohm problem? Here is the given: Particles (of mass m, and charge q), are driven through two slits that have distance d between them, in a screen that is far away (L>>d) from the...

Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...

Homework Statement Find the eigenfunctions and eigenvalues of the isotropic bidimensional harmonic oscillator in polar coordinates. Homework Equations $$H=-\frac{\hbar}{2m}(\frac{\partial^2}{\partial r^2}+\frac{1}{r}\frac{\partial}{\partial r}+\frac{1}{r^2}\frac{\partial^2}{\partial...

Homework Statement A particle with spin s=1/2 moves under the influence of a magnetic field given by: $$\vec{A}=B(-y,0,0)$$ Find the eigenvalues of the corresponding Pauli hamiltonian. Repeat the same process for: $$\vec{A}=\frac{B}{2}(-y,x,0)$$ Explain your result by relating the...

Homework Statement Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle## Homework Equations...

I just began graduate school and was struggling a bit with some basic notions, so if you could give me some suggestions or point me in the right direction, I would really appreciate it. 1. Homework Statement Given an infinite base of orthonormal states in the Hilbert space...

##\hat{v}_i=c\hat{\alpha}_i## commute with ##\hat{x}_i##, ##E^2={p_1}^2c^2+{p_2}^2c^2+{p_3}^2c^2+m^2c^4## But in classical picture,the poisson braket...

I know that clarifications about delayed choice experiment was asked million times, and I understand the idea, but I was not able to find the discussion of this particular situation anywhere, though I tried hard. This setup is described in Brian Greene's Fabric of the Cosmos book (note my...

I'm a bit confused as to what is meant by instantaneous eigenstates in the Heisenberg picture. Does it simply mean that if vectors in the corresponding Hilbert space are eigenstates of some operator, then they won't necessarily be so for all times ##t##, the eigenstates of the operator will...

From a physical perspective, is the reason why one requires that the norm of a state vector (of an isolated quantum system) is conserved under time evolution to do with the fact that the state vector contains all information about the state of the system at each given time (i.e. the...

The ground state wave-function of a 1-D harmonic oscillator is $$ \psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}). $$ a) find Average potential energy ? $$ \overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2} $$ b) find Average kinetic energy ? $$ \overline{T} =...

If all fundamental particles are zero dimensional, are atoms empty space? And they are zero dimensional, does that mean that we don't exist?