Quantum Mechanics Answers

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

a) Calculate the components of energy along x, y and z axes and the total energy for an electron in a cubical box of length 10^-9 m, if nx = 3, ny =nz =1. State the values of nx, ny and nz for two other energy states which are degenerate with this level.

Hint: Use the principle of calculation of energy of a particle in the three dimensional box. (5)

For the ground state of linear harmonic oscillator calculate average value of "x" and "x^2".

why Heisenberg's uncertainty principle is insignificant for macroscopic particles such as moving car or ball?

Find a formula that calculates amount of hits per time (in time units) with the wall (area = one square unit) for quantum gases: 1) for Fermi-gas (T -> 0), 2) for Bose-gas ( T<T_0)