2. State under which condition the following are nonzero a. (n,l,m[z\n',l',m') b. (n, l, m[x]n', l', m') c. (n, l, m[y]n', l', m')
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- 45. Let CR" be a domain and let u € C²(2). Show that u if u is subharmonic then Au 20 in 2. Hint: Assume Au(20) 0. Use 4. to deduce that -u is subharmonic in B(ro, r) which implies that u satisfies the mean value property in B(ro, r). Then conclude a contradiction.4. Describe the following energy state transition for an electron in a hydrogen atom. List the energy of the emitted photon, wavelength, its initial and final orbit. (a) n=3 to n = 1, (b) n=6 to n= 2, (c) n = 5 to n=3.
- 1. Enumerate the microstates of p3. Determine the MS and ML values for each microstate. 2. On a table of possible MS and ML values, tally the microstates in no. 1 for a particular combination of MS and ML 3. Based on the table in no. 2, determine the atomic term symbols for the allowed atomic states of p3 resulting from the coupling of orbital and spin angular momentums. 4. Arrange the term symbols in no. 3 according to increasing energy.4. Show that the internal energy, U, of an Einstein crystal is given by: 3Nhv 3Nhvexp(-ßhv) 2 1-exp(-Bhv) + U = Hint: The following identity will avoid you having to use the chain rule: d In(1− ef(x)) = −(ƒ'(x)) e²“ dx 1-eQuestion A1 Give the term used in condensed matter physics for each of the following: a) The centre of the Brillouin zone b) A method for generating a neutron beam by bombarding a heavy metal target with protons c) The group of atoms associated with each lattice point in a crystal structure d) The Fourier transform of the lattice of a crystal e) A vibrational mode whose frequency tends to zero as the wavevector approaches zero f) A model of electronic structure in which electrons move in a weak, periodic potential and do not interact with each other by the Coulomb force