1. Problems Quantum Mechanics: Lecture 111 Problems Quantum Mechanics: Lecture 11.1Consider the system of units used in high energy physics, that is, where wedefine ¯h= 1,c= 1. In this system all the physical quantities can be expressed inunits of the energy or powers of the energy.a) Express 1 s, 1 Kg and 1 m in MeV.b) Write you weight, height and age in MeV.1.2The lifetimeτof an unstable particle is defined as the time needed for theinitial number of particles to reduced to 1/eof its value, that is,N(t) =N0e−tτwhereN0is the number of particles att= 0. Knowing that the charged pions have,in their rest frame,τπ= 2.6×10−8s andmπ= 140 MeV evaluate:a) Theγfactor for a beam of 200 GeV pions.b) The lifetime in the laboratory frame.c) The percentage of pions that have decayed after travelling 300 m in the labo-ratory. If there was no time dilation, what would have been the percentage?1.3Consider the decayπ−→µ−+ν, wheremπ= 139.6 MeV,mμ= 105.7 MeVandmν= 0. Determine:a) The linear momenta of theµ−and of theνin the center of mass frame, thatis, where theπ−is at rest.b) The linear momenta of theµ−and of theνin the laboratory frame, assumingthat theνis emitted in the same direction of theπ−.c) Repeat b) assuming now that it was theµ−that was emitted in the directionof theπ−.