Assignment
Modern Physics
Q1.
Photo
Name Source
Explanation
Examples
Here, R denotes the roll number of the student.
Q2. In the Davisson and Germer Experiment, the kinetic energy of the electrons is
(70+2*R) eV. The spacing d for Ni was known from X-ray scattering to be
0.092 nm. Calculate the grazing angle, at which the Ist,2nd and 3rd order
maximum will occur.
Q3. Calculate the De-broglie wavelength of wave associated with electron
accelerated from rest by a potential difference of (5+0.1*R)V.
Q4. Calculate the energy of photon needed to excite an electron in hydrogen atom
to jump to 3rd energy level from ground level.
Q5. Calculate the wavelength and frequency of photon emitted, if the
electron de-excites from fourth to third level. What type of light will be
emitted (in term of spectrum) from the atom?
Quantum Mechanics
Q1. Consider the states |𝜓⟩ = (3 + 0.1 ∗ R)𝑖 |𝜙1 ⟩ + (2 + 0.2 ∗ R)|𝜙2 ⟩ and
|𝜒⟩ = (3 + 0.3 ∗ R)𝑖 |𝜙1 ⟩ − (4 + 0.4 ∗ R)|𝜙2 ⟩, where the two vectors |𝜙1 ⟩
and |𝜙2 ⟩ form a complete and orthonormal basis. Calculate the following.
a.
b.
c.
d.
e.
f.
⟨𝜒|𝜓⟩
|𝜓⟩⟨𝜒|
𝑇𝑟(|𝜓⟩⟨𝜒|)
𝑇𝑟(|𝜒⟩⟨𝜓|)
𝑇𝑟(|𝜒⟩⟨𝜒|)
𝑇𝑟(|𝜙⟩⟨𝜙|)
Q2. Consider the state 𝜓(𝜃, 𝜙) = 𝑒 −3𝑖𝜙 𝑐𝑜𝑠𝜃
(a) Is this state an eigen-function of
𝜕
𝜕
𝐴̂𝜙 =
or B= ?
𝜕𝜙
𝜕𝜃
(b) Check whether 𝐴̂ and 𝐵̂ are hermitian.
(c) Evaluate the expression
⟨𝜓|𝐴̂𝜙 |𝜓⟩ and ⟨𝜓|𝐵̂𝜃 |𝜓⟩.
(d) Find the commutator [ 𝐴̂𝜙 , 𝐵̂𝜃 ].