hokhani's latest activity

The uncertainty is given by: $$\langle (\Delta A)^2\rangle\langle (\Delta B)^2\rangle \ge \frac{1}{4} |\langle [A,B]\rangle|^2$$ with...

Consider a particle in an eigenstate of the Hamiltonian when the particle is in a 1D box with very large length ## L##. The operators...

By no means. It could be bouncing back and forth within the confined space very fast. Or very slow. Or not at all.

A lattice site is in fact an orbital and not a point, and the orbitals overlap to form band structure. So, the T.B Hamiltonian in...

To resolve this problem, Born-Von-Karman boundary conditions is used.

If we had already the particle confined in a very narrow 1D box (to the extent of almost a point ##x_0##), then the speed of particle...

As a peculiar thing, suppose that we have constricted a particle in a 1D box with the length ##L##. By measurement of the momentum, the...

To approve further, the variance of wave functions changes by time and so the product of the two ##\Delta##s may change by time.

Mathematically, the uncertainty principle sets a lower limit on the product of the variance in position and the variance in momentum...

"Uncertainty" as in the uncertainty principle is not even about the variance of a large number of measurements of a single observable...

From theoretical point, in a single measurement, the wave function collapses on one of the momentum eigenstates, say ##|p_o\rangle##. Do...

I think this equation says that by a single measurement you would obtain the value of momentum in the interval ##\Delta p## around...

Theoretical measurement of momentum of a QM particle is equivalent to action of momentum operator on the particle wave function. What is...

The Hamiltonian isn't something you measure, it's part of the specification of the system. Measuring energy is a separate operation...

Well (assuming free particle) starting at ##|\psi(t=0)\rangle=|x_0\rangle## you need only to carry $$|\psi(t)\rangle=e^{-i\hat H...