Optionals IAS Mains Physics: Questions 211 - 216 of 307

Let us express the Hamiltonian operator in polar coordinates as

Where is expressed as

The orbital angular momentum operator is given by

Therefore may be written as

So the three – dimensional, time independent Schrodinger equation of a article in a potential may be written as

Or

The orbital angular momentum operators and don՚t contain the radial v…

The main differences between interference and diffraction are as follows:

We know that angular momentum component operator is expressed as where I, j, k are in cycle order (i, j, k = 1,2, 3) .

Let us take commutator in cyclic order

We have

Question: 8. Prove the following identities: -

Writing the expansion of

If

if is along x and if is along y.

Let us consider has 2 components i.e.. along x and y.

If is considered …

The effective mass is defined as

The indicates that the effective mass of an electron isn՚t constant but depends on the values of . i.e.. on the shape of the curve. The variation of effective mass with k is shown in fig (1) . The effective mass is positive in the lower half of the energy band and negative in the upper half. Thus the electron behav…

If the inter atomic distance is small as compared to the wavelength of elastic waves, the crystal can be regarded as a continuum from the point of view of the wave. Based on this idea, Debye assumed that the continuum model is applicable to all possible vibrational modes of the crystal. Further the fact that the crystal consists of a finite no. (N)…

Let the electron of rest mass and electric charge be accelerated from rest by a potential to velocity , then,

Its wavelength