1. (a) The radial wavefunction for the ground state of hydrogen is given as Co R₁(r) = o exp(-¹/a₂), where a = 0.53 Å is a Bohr radius. (a) Normalize the above ав function. (b) What is the most probable value of r? (c) What is the expectation value (r)?
1. (a) The radial wavefunction for the ground state of hydrogen is given as Co R₁(r) = o exp(-¹/a₂), where a = 0.53 Å is a Bohr radius. (a) Normalize the above ав function. (b) What is the most probable value of r? (c) What is the expectation value (r)?
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Sx
Pauli spin matrices
= 1/2 (1₂6). s, = 2/2 (1₂5).
Sy
S₂ = 1/2 (19)
0
Radia wavefunctions of hydrogen R20 = -3/2² (1-1) exp(-r/2a)
R21 1
= a-3/2
/2 exp (-r/2a)
√24
Some spherical harmonics
1/2
x=(-)¹²
3 1/2
Y₁ = (2²) ¹2² c cos
Y₁¹ = F
3-)1/² sin (
87
1.
(a) The radial wavefunction for the ground state of hydrogen is given as
R₁(r) = Co exp(-r/ag), where a = 0.53 Å is a Bohr radius. (a) Normalize the above
ав
function. (b) What is the most probable value of r? (c) What is the expectation value (r)?
Betio
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