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Quantum

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Submitted By tangweitao
Words 1223
Pages 5
ELEC 9705
Quantum Devices
Session 1, 2014

Assignment 1

Student ID:3402048
Name:Weitao Tang

Part 1 – Controlling the spins of a hydrogen atom

1.1
4-dimentional Hilbert space: plus_plus = plus_minus =
0
1
0
0

minus_plus =

1
0
0
0

0
0
1
0

minus_minus =
0
0
0
1

Spin operator of electron:
Ix =
0
0.5000
0
0

0.5000
0
0
0

0
0
0
0.5000

0
0
0.5000
0

Iy =
0.0000 + 0.0000i
0.0000 + 0.5000i
0.0000 + 0.0000i
0.0000 + 0.0000i

0.0000 - 0.5000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i

0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.5000i

Iz =
0.5000
0

0
-0.5000

0
0

0
0

0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 - 0.5000i
0.0000 + 0.0000i

0
0
0
0
Spin operators of proton:
Sx =
0
0
0.5000
0

0
-0.5000

0.5000
0
0
0

0
0
0
0.5000

0.5000
0

0
0.5000
0
0

Sy =
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.5000i
0.0000 + 0.0000i

0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.5000i

0.0000 - 0.5000i
0.0000 + 0.0000i
0.0000 + 0.0000i
0.0000 + 0.0000i

0.0000 + 0.0000i
0.0000 - 0.5000i
0.0000 + 0.0000i
0.0000 + 0.0000i

Sz =
0.5000
0
0
0

0
0.5000
0
0

0
0
-0.5000
0

0
0
0
-0.5000

1.2
The values of eigenvectors: phi_1 = phi_2 =
0
1
0.7071
0
-0.7071
0
0
0 phi_3 = phi_4 =
0
0.7071
0.7071
0

0
0
0
1

The values of eigenvalues:
E_1 =
E_2 =
-6.6916e+09
2.2305e+09
Spin expectation values:

E_3 =
2.2305e+09

E_4 =
2.2305e+09

T0_ztot =
0
T1_ztot =
1
T2_ztot =
0
T3_ztot =
-1
sigma_ztot =Sz+Iz
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
Discuss the nature of the eigenstates. Can you recognize what is the spin state of the electron and the nucleus in each of the eigenstates (hint: calculate the expectation values of all the

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