Quantum Mechanics Answers

Prove the following:

i. [AB,C] = [Â,C]B + Â[B,C]

ii. ihq = qH - Hq given that H = mq

Show that the uncertainty in the measurement of a physical quantity "f" is equal to the following expression:

"\u0394f=\u221a(\u27e8f^2 \u27e9-\u27e8f\u27e9^2 )"

the perturbation H'=bx^4 is added to one dimensional harmonic oscilllator potential v(x)=1/2mw^2x^2.find the correction to ground state energy to first order in b

In early version of double slit experiment discussed,carnal and mlynek use helium atoms ( from reservoir maintained at 295k) that exit the nozzle after expansion with wavelength = 0.56 A (a) what is the speed of the helium atoms

The speed of a train is reduced uniformly from 15 m/s to 7 m/s while traveling a distance of 90 m. How much farther will the train travel before coming to rest, provided the acceleration remains constant? The acceleration is -9.81 m/s2

** Estimate the energy splitting between the lowest two levels for an electron in a three-dimensional cube-shaped potential box with the side length 10 nm.

1◦ 1 meV

2◦ 10 meV

3◦ 100 meV

4◦ 0.11 eV

5◦ 0.22 eV

6◦ 1.12 eV

Estimate the energy splitting between the lowest two levels for an electron in a three-dimensional

cube-shaped potential box with the side length 10 nm.