Electrostatics and Magnetostatics

For a spin-s particle, in the eigen basis of 5%. S, the expoctation value (sm|S; (sm) is (A) - Nfs(s+1)-m'} (B) s°(s(s+1)-2m*) 2 (C) 1°{s(s+1)-mi*} (D) n'm PH 11/24 2010 0.45 A paricle is placed in a region with the porenial V(x)==xx'- 3'*", where k.A>0. (A) r=D and x=ê are points or stable equiliorium (B) x = 0 is a point of stable cquilibrium and *=* is a point of unstable equilibrium (C) x =0 and x =. - are points of unstable equilibrium (D) There are no points of stable or únstable equilibrium 0.46 A a" meson at rest decays into Iwo pholons, which move along the x- axis. They are both detecied simultaneously after a time, t = 10 s. In an inertial frame moving with a velocity V = 0.6c in the direction of one of the photons, the lime interval belween the lwo detections is (A) 15 s (B) 0s (C) 10s (D) 20 s 0.47 A particle of mass m is confined in an infinite porential well: if O< x<L. V(x)=1 otherwise. I is sulbiected 1o a perurtbing porential V,(+) - V,sin(2Zt) Vợ) within the well. Lel E"" and E'" be the corrections to the ground state energy in the first and second order in V, Vр(х) respectively. Which of the following are true? L (A) E"' = 0; E3<0 (В) Е"> 0; E:=0 (C) E"'= 0; E*" depends on the sign of Vo (D) E'" <0: E3<0 Common Data Questions Common Data for Questions 48 and 49: In the presence of a weak magnetic field, alomic hydrogen undergoes the transition: 3Py →'Sy, by emision of radiation.

Options:

• (A) E"" = 0; E3<0
• (B) E" >0;
• (D) E"' <0: E" <0 Common Data Questions Common Data for Questions 48 and 49: In the presence of a weak magnetic field, alomic hydrogen undergoes the transition: 3P% → 'Sy, by emission of radiation.
• (C) F"'= 0; E" depends on the sign of Vo