In Delayed choice quantum eraser experiment entangled photons are sent through different paths. They do not reach different detector at different times. The one arriving early is called a signal photon. The photon that arrives at its destination at later time randomly goes through one (using the ...

Definition of Invariant subspace In mathematics, an invariant subspace of a linear mapping T : V → V from some vector space V to itself is a subspace W of V that is preserved by T; that is, T(W) ⊆ W (Definition from Wikipedia) Q1.My question is how to justify the following argument using the...

sir/mam i found a new theoy of connactions between time,gravity, energy, mass, force....... but I am in 12th science jst 17 year old.i dont know what to do now please help me if possible

At a roughly high school mathematics level I understand (a) that relativity is modelled using four-dimensional spacetime curved by mass/energy with particles/light following the shortest possible paths (aka geodesics), and (b) quantum mechanics is modelled on the complex plane where the square of...

Consider the cosmic rays. The muons can travel 15000 meters through the atmosphere and get down to sea level. If this is not a quantum mechanical effect, its penetration depth is determined by the mean free path. The mean free path is about 68 nm on the sea level. Actually, by classical mecha...

The time-dependent Schrodinger equation is given as $$i \hbar | \psi(t) \rangle = \hat{H} | \psi(t) \rangle. $$ To find how the states evolve in time we want to find the linear operator $\hat{U}(t,t_0)$ such that $$| \psi(t) \rangle = \hat{U}(t,t_0)| \psi(t_0) \rangle.$$ Substituting into Schrod...

The most general form of the Shrodinger equation is $$i \hbar \frac{d}{dt}| \psi(t) \rangle = \hat{H} | \psi(t) \rangle$$ but we also have the Schrodinger equation when projected onto the position basis given as $$i \hbar \psi(r,t) = i \hbar \langle r | \psi(t) \rangle = \langle r | \hat{H}| \psi...

In the area of the time-dependent perturbation theory, if we have $$\hat{H}(t) = \hat{H}_0 + \hat{V}(t).$$ The Schrodinger equation is $$i \hbar \frac{d | \Psi(t) \rangle}{dt} = (\hat{H}_0 + \hat{V}(t))| \Psi(t) \rangle$$ where in the Shrodinger picture we have $$|\Psi(t) \rangle = \sum_n c_n(t)e...

Consider the potential $V(x)=1/x+1/(1-x)$ on the interval $[0,1]$, and the corresponding Schrödinger operator $-\frac{d^2}{dx^2}+V(x)$. Is this operator essentially self-adjoint? Can we compute an explicit analytical representation for its eigenvalues and/or eigenfunctions? Is there anything w...

First of all read till the end. Do not mark as duplicate before finishing. The answer to the question above is that photons interact with molecules in the water which takes some time causing the net speed to drop. But lets remember something. For an object to be transparent the incoming light sho...

In order to obtain the Jaynes-Cummings Hamiltonian, the RWA is applied to the Hamiltonian: $$H=\frac{1}{2}\hbar\omega_0 \sigma_z+\hbar\omega \hat{a}^{\dagger}\hat{a}+g\hbar(\sigma_{+}+\sigma_{-})(\hat{a}+\hat{a}^{\dagger}),$$ under two conditions: the near resonance $\omega_0\approx\omega$, and t...

I have a question which reads: Let \begin{bmatrix} {E_0} & 0 & A \\ 0 & E_1 & 0 \\ A & 0 & E_0 \end{bmatrix} be the matrix representation of the Hamiltonian for a three-state system with basis states $|1>, |2> \mbox{and } |3>$. a. If the state of the system at t...

How is it possible to show that the probability that the momentum $\zeta$ of the particle belongs to the interval $(a,b)$ is $\int_a^b|\hat{\psi}(\zeta)|^2 \, d\zeta$ where $\hat{\psi}$ is the Fourier transform of $\psi$? $\psi$ is the wave-function. Thank you for your help in advance!