ies, do not forget that each particle has twO possible orientations of its spin.] (b) Assuming that there are six particles in the box, draw an energy-level diagram similar to Fig. 10.6(b), showing the distribu- tion of particles that gives the state of lowest energy for the system as a whole. (c) Do the same for the case where there are ten particles in the box. of a helium atom. (a of a helium atom (inm mation where you ig force between the t proximation you can if it were in a hydro just the sum of the answer in part (a) sh the system is boun ignored the positive pulsion between the estimate of this addi the electrons to be in SECTION 10.5 (Fermions and Bosons*) 10.12. The wave function for two spinless particles would have the form = (x1, x2). (a) Give an example of such a function that is symmetric under particle ex- change and normalizable (integral of (x1, x2) over all x1 and all x2 is finite). (b) Give an example that is antisymmetric. (c) Give an example that is neither symmetric nor antisymmetric. %3D aB/2 (the appropriat with Z = 2). To mini trons would move a 10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec- trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to always on opposite si apart. Use this semi potential energy of t with your answer to energy of the He ato value of -79 0 e

ies, do not forget that each particle has twO possible orientations of its spin.] (b) Assuming that there are six particles in the box, draw an energy-level diagram similar to Fig. 10.6(b), showing the distribu- tion of particles that gives the state of lowest energy for the system as a whole. (c) Do the same for the case where there are ten particles in the box. of a helium atom. (a of a helium atom (inm mation where you ig force between the t proximation you can if it were in a hydro just the sum of the answer in part (a) sh the system is boun ignored the positive pulsion between the estimate of this addi the electrons to be in SECTION 10.5 (Fermions and Bosons*) 10.12. The wave function for two spinless particles would have the form = (x1, x2). (a) Give an example of such a function that is symmetric under particle ex- change and normalizable (integral of (x1, x2) over all x1 and all x2 is finite). (b) Give an example that is antisymmetric. (c) Give an example that is neither symmetric nor antisymmetric. %3D aB/2 (the appropriat with Z = 2). To mini trons would move a 10.13. (a) Consider the helium atom to be a fixed point nucleus (charge 2e) with two spin-half fermion elec- trons. What is the degeneracy of its ground state? (That is, how many independent states of the whole atom have the ground state energy?) (b) Suppose instead that the electron was a spin-half boson. (It is an experimental fact that all spin-half particles are fermions, but there is nothing to always on opposite si apart. Use this semi potential energy of t with your answer to energy of the He ato value of -79 0 e