, the photon could convert into an
pair. However, this
process cannot occur in the empty space. Please explain the reason. (10%) What is the
threshold frequence of photon for such a process? (10%)| 所組別： | 應用物理學系 | 科目： | 近代物理 | 考試時間： | 6月14日第2節 |
| Ⅰ. | Please give a detailed description of length contraction and time dilation in special relativity. (10%) |
| Ⅱ. | In the process of pair production, the photon could convert into anpair. However, this
process cannot occur in the empty space. Please explain the reason. (10%) What is the
threshold frequence of photon for such a process? (10%) |
| Ⅲ. | Consider a system with the Hamiltonian Suppose that the system is in a state described by the normalized wavefunction  |
| (1). | If we try to measure the energy of the system, what is the resultant value we obtain? (10%) |
| (2). | Suppose that there is a small perturbation to the system, please find the energy of
the system up to the first order in  .
(10%) |
| Ⅳ. | Consider a hydrogen atom with the Hamiltonian |
| (1). | Please give a set of quantum numbers that we can use to describe the
state of the system. (These quantum numbers must include the operators  and  ) (10%) |
| (2). | Please give another set of quantum numbers, including the operator of
total angular momentum along the z-axis and the operator  ,
that we can use to describe the state of the system. (10%) |
| (3). | The eigenvalue of energy of the hydrogen atom is given by where  is the fine structure
constant,  Consider the bound states of a system consisting of a electron and positron. What are the possible eigenvalues of energy? (10%) |
| Ⅴ. | Consider the spin states of two electrons. There are four possible states, (  ,  ),
( , ), ( , ),
and ( , ). |
| (1). | If we try to use the eigenstates of  and
Sx to describe the spin state with  and  , what are the possible
states? (10%) |
| (2). | What are the transformations between the possible states given in (1) and the four possible states in the above? (10%) |