Let
*
φ
_{
nℓm
}
*
(

*
ψ
*
(
**
r
**
)=

(a) Find the
normalization constant
*
C
*
. Can
*
C
*
be complex, real or imaginary?

(b) What is the expectation value of the Hamiltonian for the H-atom in this superposition of states? Calculate your answer in units of eV.

In parts (c) and (d), find the following expectation values:

(c) Find
á
**
L
**

(d) Find
á
*
L
*
_{
z
}
ñ
.

(e) What is
the probability of finding the electron in the
*
φ
*
_{
210
}
(
**
r
**
)
state?

(f) If the
electron is in the
*
φ
*
_{
100
}
(
**
r
**
) state, find the
radius at which the radial probability density is a maximum. How does this
compare with the Bohr radius? What is the significance?

(g) Find the
wavefunction
*
ψ
*
(
**
r
**
,