ECE 4184 - Applied Quantum Mechanics for Engineers
Review of classical mechanics, the simple harmonic oscillator. Schrodinger equation, barrier tunneling, resonant tunneling, and quantum wells. Mathematical foundation of quantum mechanics, Dirac notation and representations, observables, eigenstates and diagonalization. Quantum postulates and its application to two-level systems, harmonic oscillators, creation and annihilation operators. Time evolution of a Hamiltonian. Dynamics of spin and two-level atoms. No cloning theorem and the concept of entanglement.
Why take this course?
Quantum mechanics underpins a series of key technological developments that occurred in the past 75 years starting with the developments of transistors and laser. Still these key devices in their continued development did not require knowledge of quantum mechanics to execute their design and development. But today a series of new devices and systems in communications, sensing and computing are directly based on the principles of quantum mechanics, including quantum key distribution for secure communication systems and sensors such as magnetometers and ultimately quantum computer elements. Therefore, a working knowledge of the machinery of quantum mechanics, concepts and the mathematical formalism is needed for the next generation of practicing electrical engineers.
- Calculate the eigenvalues and eigenfunctions of the free particle, infinite potential square well, and harmonic oscillator
- Compute the transmission and reflection coefficients of a plane wave impinging on a potential barrier
- Illustrate physical situations using the mathematical language of complex vectors and the Dirac notation
- Interpret the results of experiments in terms of quantum theory
- Apply quantum theory to interpret experimental results
- Predict probabilities of measurement outcomes
- Compute the future state of a system from its initial state and its Hamiltonian