Selected chapters of quantum mechanics for modern engineering

Week 1:

History of quantum mechanics. Wave packet. Schrödinger equation. Properties of wave function, normalization. Averages and operators. Superposition of states, measurement, commutators. Schrödinger equation

Week 2:

Infinite well. Delta-barrier, matching wave functions. Dirac’s bra-ket notation. Operators in Dirac’s notation, Hermitian conjugation. Harmonic oscillator via ladder operators.

Week 3:

Qubit and Bloch sphere. Quantum superposition of N qubits. Overview of quantum computing algorithms and their advantage as compared to classical algorithms. Quantum teleportation. Quantum decoherence of many-qubit system and quantum error correction. Physical realization of quantum computers: difficulties and advances.

Week 4:

Superconductivity: Discovery. Main Properties, Meissner's and Josephson's effect. Types of supercoductors, Vortices. Applications of superconductivity. Summary and theoretical explanation.

Week 5:

Modeling a realistic quantum system: resonant microwave cavity coupled to qubits array via the gauge-invariant quantum phases. Mapping on the infinitely coordinated Ising spin-chain of spins-½. Holstein-Primakoff representation. 1st-order quantum phase transition into dipolar ordered state. Metastable states of the spin-chain: bound states of light.

Week 6:

Emergence of instantonic ‘pairing boson’ and high-Tc superconductivity. Negative energy of the ‘antiferromagnetic’ instantons. Zero-mode of instantonic ‘crystal’ along Matsubara time axis as the ’pairing boson’ in the Eliasberg-like equations. Why AF instantons behave as a ‘hidden order’. Spin excitations of the instantonic ‘crystal’ — hourglass modes?.

Week 7: Final Exam