Question

Consider a trial wavefunction for an electron in H atom in the following form º(r) = re-ar where a is an adjustable parameter. Optimize a so that you obtain the minimum energy (i.e., find the extremum by imposing .. (E) = 0). How does the minimum energy compare to the ground state energy of an electron? Hint: n! IX"e-ax dx = for α> 0 Δ η Ε Ν an+1 Integration of function f(r,0,0) in spherical coordinates: - po T 27 f(r,0,0)ra sin İdodödr Jo Jo Jo

Answer 1

Q: $(~) = re-ar Lor •/ - h. . (4.07 Am · <e>= SY.(.) V p) - ** tno dodo * <** S* (29) Te vagy ... [5*offie op <ED = (ock"). vores La flor ce -a+ e les-ode-fo) = -de-do-6r(-de-pat -dept) :-47- 200-47 <E>= -h 4 *Carlore-po_222-40) redr.

:e-** - 273..2-200 dr. - Jus: mm, e dn = ni Qh+1 - h' m 1+1 X3x 2x1). *3 x 2x1). - m ago. a5 28.(3xQx1)] 294.74 .- Program - $ ] <E> = 0 — with any value of a. The value of <E> ... one will be Zero, (according to calculations) - Energy of electron in Ground State = -13.6 z