Calculate (x) and (px) for the ground state harmonic oscillator eigenfunction.
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A spaceship is receding from the earth at a speed of 0.3c. A light on the spaceship emits light of wavelength λ = 4500 Å which appears blue to a passenger on the spaceship. What colour would the light appear to a person on earth?
If σ x, σ y and σz are three components of a Pauli spin matrix σ, then show tha
[σ x , σ y ] = 2i σ z ; [σ y , σ z ] = 2iσ x
Two events happen simultaneously in the frame S at a distance of 3.0 light years apart. In the frame S′, which is moving with a speed v relative to S, the distance between these events is 3.5 light years. Calculate (i) v and (ii) the time interval between these events in the frame S′
Consider nuclei with small mass number A such that N = Z = A/2 . Neglecting
pairing term (∈) show that semi-empirical formula is given by
Obtain the value of A and Z for which binding energy per nucleon (BE / A) is maximum. Take β = 17.8, δ = 0.71.
In a region of space a particle of mass m has a wavefunction:
where a is a positive constant. Calculate:
i) the normalization constant N
ii) the potential energy of the particle if the total energy of the particle is zero.
Calculate the de Broglie wavelength of an electron accelerated by a potential of 1000 V. Also calculate the wavelength of the X-rays that would be produced when these electrons strike a solid.
Determine the commutator [Lz ,Ly ] .