[試題] 100上 陳智泓 量子物理上 期末考
課程名稱︰量子物理上
課程性質︰物理系系必修
課程教師︰陳智泓
開課學院：理學院
開課系所︰物理系
考試日期（年月日）︰01/10/12
考試時限（分鐘）：120min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(10%) Compute the commutation relation, [e^ax, p], where a is a real
constant.
^
2. An operator A, representing observable A, has two normalized
eigenstates Ψ1 and Ψ2, with eigenvalues a1 and a2 respectively.
^
Operator B, representing observable B, has two normalized eigenstates
ψ1, ψ2, with eigenvalues b1 and b2. The eigenstates are related by:
1 1
Ψ1=---(4ψ1+3ψ2), Ψ2=---(3ψ1-4ψ2)
5 5
(a) (5%) Observable A is measured, and the value a1 is obtained. What
is the state of the system (immediately) after this measurement?
(b) (10%) If B is now measured, what are the possible results, and
what are their probability?
(c) (10%) Right after the measurement of B, A is measured again.
What is the probability of getting a1?
3. The Hamiltonian for a certain three-level system is represented by
matrix
^ ╭1 0 0╮
H= hw/2│0 1 0│
╰0 0 2╯
Two other observalbes, A and B, are represented by the matrices
^ ╭0 1 0╮
A=λ│1 0 0│
╰0 0 2╯
^ ╭2 0 0╮
B=μ│0 0 1│
╰0 1 0╯
where wψ,λ,μ are positive real numbers.
^ ^ ^
(a) (15%) Find the eigenvalues and (normalized) eigenvectors of H,A,B
(b) (15%) Suppose the system starts out in the generic state
╭c1╮
|S(0)>=│c2│
╰c3╯, ^ ^ ^
with |c1|^2 +|c2|^2 +|c2|^2 =1. Find the expextation value of H,A,B.
(c) (25%) What is |S(t)>? If you measured the energy of this state
(at time t), what values might you get, and what is the probability of
each? Answer the same questions for A and B.
4. (10%) Quarks carry spin 1/2. A quark and its antiparticle bind together
to make a meson. Assume the orbital angular momentum in a meson between
the quark and the anti-quark is l=1. What angular momentum states are
possible for meson?
5 (0%) 祝大家新年愉快，寒假過得充時開心！
註:第五題不是我自己打的...老師是好人。
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01/10 15:22, , 1F
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01/13 11:03, , 2F
01/13 11:03, 2F