We introduce the main mathematical set up of discrete quantum mechanics as well as basic quantum mechanical concepts, such as quantum states, observables and time evolution of quantum systems. We also present the notions of spin operators, spin states and composite systems and basic concepts on quantum computing. We then discuss the time dependent and time independent Schrödinger’s equation for space continuous systems and solve prototypical quantum mechanical systems.
1. Fundamental concepts: (1.1 Introduce the basic notions in formulating quantum mechanics: linear algebra, vector spaces, eigenvalues & eigenstates. 6 lectures)
2. Basic quantum mechanics (2.1 Quantum states and observables, time evolution of quantum systems 6 lectures)
3. Spin operators & Composite systems (3.1 Introduce the notion of spin operators and spin states. Derive the tensor product of matrices and vectors and construct composite quantum mechanical systems. Introduce Schmidt’s decomposition 6 lectures)
4. Quantum computing (4.1 Introduce basic quantum circuits and quantum algorithms. 6 lectures)
5. The Schrödinger equation (5.1 Study the time dependent and the time independent Schrödinger equation for continuous quantum mechanical systems. Study fundamental quantum mechanical systems 6 lectures)
By the end of the course, students should be able to do the following:
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SCQF Level: 10
Credits: 15