Abstract: The representation and calculation of matrix mechanics is a very important element

in the quantum mechanics course. The two-level system serves as a simple example to deepen

students' understanding of matrix me- chanics. However，the current textbooks give rather limited

attention to the two-level system. In this paper，we intro- duce a system in the research frontier

of quantum information: the charge qubit. In the teaching，the system is first modeled using a

Hamiltonian operator to describe the occupation and tunneling processes of a single electron in two

quantum dots. Then，the state and the time evolution of the system are obtained by three methods

such as energy ei- genfunctions representation，solving the time-dependent Schrödinger equation and

solving the equation of motion for the expectation value of an operator. Finally，by comparing the

theoretical analysis and experimental results，students can find that the theory is consistent with

the experiment. Thus these teaching contents can help students to grasp more intuitively

and deeply the quantum mechanical laws and calculations with the matrix mechanics representation.

Key words: two-level system, charge qubit, matrix mechanics