Quantum Mechanics Answers

The displacement of a particle along the X-axis is given as
x=5t2+1
, where x is in metres and t in seconds. Calculate its instantaneous velocity 2 s.

46 m/s

40 m/s

20 m/s

25 m/s

a man walks 5.0m due east, and then 10.0m N30oE find his resultant displacement?

Find the average value of Px. <Px> for n=1 state of a particle in a one dimensional box of length 'l'. Comment on your result.

Consider a charged particle bound in the harmonic oscillator potential V (x) =½mω²x². A weak electric field E is applied to the system such that the potential energy is shifted by an amount H'=-qEx.

(a) Calculate the energy levels of the perturbed system to second order in the small perturbation.
(b) Show that the perturbed system can be solved exactly by completing the square in the
Hamiltonian. Compare the exact energies with the perturbation results found in (a).

Calculate the first-order energy corrections for all levels of an infinite square well potential
(between x = 0 and x = L) with a perturbation H' = αx(L-x)

A sailboat moves north for a distance of 10.00 km when blown by a wind from the exact southeast with a force of 2.00 × 104 N. The sailboat travels the distance in 1.0 h. How much work was done by the wind? What was the wind’s power? Your response should include all of your work and a free-body diagram.

In compton effect, when scatterring angle of x-rays is zero,hence there is no change in frequency and energy.
but in this case elecron recoils at 90 degrees why?
From where does it get the energy to recoil?

If the function psi1 & psi2 are solution of Schrödinger wave equation for a particle , then prove that a1psi1+a2psi2 is also a solution of same equation, where a1 & a2 are arbitrary constants.

now that we know the god particle really exist, how does it means electron have a mass when it circle around the orbit? can we use this to explain plancks constant in a more pictorial way, than just e=hv?

i read the graphs of the black bodyy radiation on frequency and temperature. and how planck just come up with the equation because frequency doesnt change much with inccrease of temperature in the experiment, am i understanding it correctly?

and the noble price of the atom equation,which In 1913 Niels Bohr published the Bohr model
L=n(h/2pi) how is momentum define in quantum mechanic, can it also be see as mass times angular velocity? or how is it defined? and how come there is a pi in the equation?

any good book that gives the insight of these equation i could have a look?

a) Using molecular orbital theory, draw the energy patterns of the following:
i) B2
ii) O2
Comments on the difference between the two patterns