Answer Happy

Question 3: Nuclear Potential Well (See Supplement 1- Quantum Mechanics) Consider a non relativistic particle (masse m, energy E< 0) in a 1D finite rectangular potential well of depth Ve (Vel > IEI) and width The energy states are obtained by solving a system of 2 transcendental equations, namely: atana = √P²-a² and -acota = √P²-a² where akap²_mVa² and k₂ is the wavenumber of the wavefunction inside 24² the well. The solution of this system of equations is obtained graphically and figure 1 shows this solution for P = 4. Take m=940 MeV/c and a = 1.5 F. a) What is the value of Ve? b) How many eigenenergies does this system have? c) What is the energy of the ground state of this system? d) Compute the wavenumber k₂. e) Compute the wavenumber of the wave outside the well k f) Explain, in your own words, why this potential is not realistic for a nuclear potential. 4.0 3.5 tana tana 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0 0.5 -a cota P²_a²¹ 1.0 1.5 1 of 35 3.0 3.5 4.0