quantum mechanics and simple quantum mechanical systems

Question 1

show that the ratio of debroy is not dependent on mass of particle only dependent on energy

Question 2

what is common to all these particles in alpha decay

Answer 2

Energy can be limitless

Question 3

energy of electron, and KE

Answer 3

E = sqrt(pc^2+(mec^2)^2)

KE=E−mec^2

Question 4

Kpe=moc^2 formula

Answer 4

lamda = h/sqrt(2mk)

Question 5

hydrogen is what system

Answer 5

a spherical system

Question 6

what is frustrated total internal reflection

Answer 6

if gap is small between two prisms when total internal reflection happens light shouldn’t go, but they go similar to quantum tunneling,

Question 7

difference btw wave function and eigen values

Answer 7

𝚿(x,t) when it involves time = wave function
𝚿(x) => eigen function

Question 8

fundamental to why larger bodies like bullets dont show interference, small quantum bodies
ex: 𝚿=𝚿1+𝚿2

Answer 8

since the wave lenght is very small for large bodies

Question 9

when will a parity show up

partity 𝚿(-x) = +-𝚿(x)

Answer 9

a parity will only show up if the potential well is only symmetric about the origin

Question 10

will you get a shift if you if use visible light using compton shift formula

Answer 10

no, wavelenght for visible light(average) => 500nm
2.48 ev

2h/moc = delta h mac
=22.24210^-24
this is such a minute wavelenght

Question 11

classical and quantum differences ISA, IM or 2M

Answer 11

classical:
- continuous energies
- cannot go beyond turning points
-minimum e can be 0
-shape of that of a bowl

quantum:
- discrete energies
- beyond turning point
- minimum cannot be 0
- depends on Quantum number

Question 12

what polynomial depends on eigen functions and eigen values of it

Answer 12

Hermite polynomial
ψ=Ae^(-x^2/2)* Hn(v)

H=(-e^x^2*(-2xe^-x^2))

Question 13

what is degeneracy, and how many states for 1,2,3, 2, if nx=ny, nx not equal to ny
IMP ISA repeated

Answer 13

degeneracy: many different states having the same energy

1,2,3=6
2=4
nx=ny=1 state
nx not equal to ny = 2 state

Question 14

conculsion on H atom using Schrodingers equation

and H atom definiton

Answer 14

orbits are not present its orbitals
no definite radius(shell)

energy is quantised

angular momentum is quantised

H atom= free particles dont have quantised energy

r=√x^2+y^2t+z^2
x=rsinθcosΦ
y=rsinθsinΦ
z=rcosθ

0<=r<∞
0<=Φ<=2*pi
0<=θ<=pi

∂^2ψ/∂x^2
+∂^2ψ/∂y^2
+∂^2ψ/∂z^2
2 μ/∂x^ ħ^2[E+e/4piϵor]ψ
L2=meħ
L=r*p, L=mv

Question 15

Anharmonic definiton

Answer 15

the curve is not symmetric about the line, real oscillators are always Anharmonic, tiny energy particles can be Harmonic

Question 16

Density states formula and draw graph ISA and fermi energy formula

Answer 16

g(E)=pi/2(8m/h^2)^3/2E^1/2

E=h^2*n^2/8mL^2
Eo=h^2/8mL
R^2=nx^2+ny^2+nz^2