Download Tutorial_questions_for_PHY_305

Tutorial questions for PHY 305
1. Using De Broglie hypothesis show that 𝜆 =
ℎ
√2𝑚𝑒𝑣
2. At time t=0 a particle is represented by the wave function
𝑥
𝜓(𝑥, 0) = 𝐴 𝑎 , 𝑖𝑓 0 ≤ 𝑥 ≤ 𝑎 where A, a are constant. Find the normalize wave function.
3. Explain the term uncertainty principle and write the uncertainty relation for position and
momentum
4. Write the uncertainty relation for energy and time.
5. State the postulates of quantum Physics.
6. Derive the time dependent Schrodinger equation from operators formalism.
7. Use the time dependent Schrodinger equation to derive the time independent Schrodinger
equation
8. Obtain the expression for the wave function of a particle in an infinite potential well.
9. State the three pillars of quantum Physics
10. Find the expectation value of the position of a particle in an infinite potential well.
11. Given that 〈𝑥〉 =
𝑎
, 〈𝑥 2 〉 =
2
𝑎2
3
−
𝑎2
2𝑛2
𝜋2
𝑛𝜋 2
, 〈𝑝〉 = 0, 〈𝑝2 〉 = ℏ2 ( 𝑎 ) .
ℏ
Show that Δ𝑥Δ𝑝 ≥ 2
12. An electron in the n=2 energy level of hydrogen remains there for 80ns before moving
down to energy level n=1.
i.
Determine the uncertainty in the energy released by the electron in the transition.
ii.
Determing the fraction of energy that this represents with respect to the total
energy released by transition of electron. (Take 𝑅 = 1.097 × 107 𝑚−1 )
13. Given that the wave function for a particle in an infinite potential well is 𝜓0 = 𝐴𝑠𝑖𝑛
Obtain the normalize wave function.
14. An electron is moving in a rigid box that has a width of 0.3nm.
i.
Find the amplitude of wave produced
ii.
Find the minimum energy of the electron
iii.
Find the minimum velocity of the electron
iv.
Find the expression for the wave function of electron for 𝑛 = 1
𝑛𝜋𝑥
𝑙
.