1
The following wave function (in which A and B are numbers not functions of x or
E1 t
E1 t
t) (x, t) = A1 (x)e ~ + B2 (x)e ~ is a linear combination of two solutions of the time
En t
dependent Schrdi
1
Using the ve-term linear trial function
in Table I below
i
1
2
3
4
5
=
q5
i r2
i=1 Ci e
with the exponents
i
33.865
5.09479
1.15879
0.32584
0.1027410
Solution:
Mathematica Code:
Clear[i, j, n, A, H,
1-7
Sirius, one of the hottest known stars, has approximately a blackbody spectrum
with max = 260nm. Estimate the surface temperature of Sirius.
Solution:
T
=
= T =
hc
4.96511kT
2.8977685103 m K
2601
1a
Using atomic units, for the quantities in the general formula for the energy
Z2
e2
levels of a one electron atom, En = 2n2 a0 40 , show that the energy of the helium ion
(He+ , with Z = 2) in its g
1a
Show that
Solution:
is 0.
s
x2 dx
xe
=0
The integrand is an odd function, and it is integrated over symmetric limits, so the answer
Beyond that, to evaluate over arbritary limits, let u = x2 = du
1
Find the values of the following commutators for the hydrogen atom Hamiltonian. Only very little algebra is required, because you may use the values of any of the
angular momentum commutators we wro
1
The internuclear distance of the 12 C 16 O molecule is 1.1283 angstroms. Look
up the masses of these isotopes of the atoms on the NIST website(http:/physics.nist.
gov/PhysRefData/Compositions/index.