With this Postgraduate certificate in Quantum Physics, you will gain the necessary knowledge to develop projects in the field of communication or computing"

Energy production, ultracold atoms, trapped ions or photonics are currently a field of development for engineering professionals who wish to immerse themselves in the field of Quantum Physics. The essential knowledge on this branch of science has undoubtedly contributed to current communications, to the promotion of new technologies and to the progress of other disciplines. 

Understanding matter at very small scales: at molecular, atomic and even smaller levels is key for the engineers who wish to advance in their career, either by implementing their own ideas or by participating in projects in renowned companies. For this reason, TECH has created this Postgraduate certificate in Quantum Physics, in which, in just 12 weeks, the professional will gain the knowledge required to thrive in their field. 

A program where students, from the beginning, will learn the main concepts of this specialty, the main laws that govern it, its postulates and the problems that can be solved by applying quantum mechanics. For this purpose, it has multimedia teaching resources that can be easily accessed 24 hours a day, from any computer, tablet or cell phone with Internet connection. 

The professionals are thus facing an excellent opportunity to study a 100% online and flexible program, that allows them to combine their work and/or personal responsibilities with quality education. In addition, the Relearning method, used by TECH in all its programs, will help reduce the long hours of study, which are more common in other teaching systems. 

Obtain the fundamentals of Quantum Physics you need to thrive in your engineering career"

This Postgraduate certificate in Quantum Physics contains the most complete and up-to-date program on the market. The most important features include:

• Practical case studies are presented by experts in Physics
• The graphic, schematic, and practical contents with which they are created, provide scientific and practical information on the disciplines that are essential for professional practice
• Practical exercises where the self-assessment process can be carried out to improve learning
• Its special emphasis on innovative methodologies
• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments
• Content that is accessible from any fixed or portable device with Internet connection

In this program, you will be able to learn the Wentzel-Kramers-Brillouin (WKB) method, comfortably from your computer or tablet with Internet connection"

The program’s teaching staff includes professionals from the sector who contribute their work experience to this educational program, as well as renowned specialists from leading societies and prestigious universities.

The multimedia content, developed with the latest educational technology, will provide the professional with situated and contextual learning, i.e., a simulated environment that will provide immersive education programmed to learn in real situations.

This program is designed around Problem-Based Learning, whereby the professional must try to solve the different professional practice situations that arise throughout the program. For this purpose, the student will be assisted by an innovative interactive video system created by renowned and experienced experts.

This is a 100% online program that is compatible with the most demanding professional responsibilities"

Click and enroll for a program that will teach you the application of the postulates of quantum mechanics"

The syllabus of this program has been designed to obtain the most advanced and relevant information about Quantum Physics in only 12 weeks. Thus, after an introduction to the origins of this branch of science, professionals will learn about the postulates of quantum mechanics, its applications, dynamics, the harmonic oscillator or the method (WKB). For this purpose, they will also have access to a library of resources available 24 hours a day and to which they will have easy access from a computer or tablet with Internet connection.

Thanks to the case studies of this program, you will delve into Spin in a more practical way"

Module 1. Quantum Physics

1.1. Origins of Quantum Physics

1.1.1. Blackbody Radiation
1.1.2. Photoelectric Effect
1.1.3. Compton Effect
1.1.4. Atomic Spectra and Models
1.1.5. Pauli Exclusion Principle

1.1.5.1. Zeeman Effect
1.1.5.2. Stern-Gerlach Experiment

1.1.6. Broglie Wavelength and the Double Slit Experiment

1.2. Mathematical Formulation

1.2.1. Hilbert Spaces
1.2.2. Dirac Nomenclature Bra - ket
1.2.3. Internal and External Product
1.2.4. Linear Operators
1.2.5. Hermetic Operators and Diagonalization
1.2.6. Sum and Tensor Product
1.2.7. Density Matrix

1.3. Quantum Mechanics Postulates

1.3.1. Postulate 1º: Definition of Status
1.3.2. Postulate 2º: Definition of Observables
1.3.3. Postulate 3º: Definition of Measurement
1.3.4. Postulate 4º: Probability of Measurement
1.3.5. Postulate 5º: Dynamics

1.4. Apply the Postulates of Quantum Mechanics

1.4.1. Probability of Results: Statistics
1.4.2. Indeterminism
1.4.3. Temporary Evolution of the Expected Values
1.4.4. Compatibility and Commuting of Observables
1.4.5. Pauli Matrices

1.5. Quantum Mechanics Dynamics

1.5.1. Representation of Positions
1.5.2. Momentum Representation
1.5.3. Schrödinger Equation
1.5.4. Ehrenfest Theorem
1.5.5. Virial Theorem

1.6. Potential Barriers

1.6.1. Infinite Square Well
1.6.2. Finite Square Well
1.6.3. Potential Step
1.6.4. Delta Potential
1.6.5. Tunnel Effect
1.6.6. Free Particle

1.7. Simple Harmonic Oscillator

1.7.1. Analogy with Classical Mechanics
1.7.2. Hamiltonian and eigenvalues of energy
1.7.3. Analytical Method
1.7.4. Blurred Quantum
1.7.5. Coherent States

1.8. 3D Operators and Observables

1.8.1. Review of Calculus Notions with Several Values
1.8.2. Position Operator
1.8.3. Linear Momentum Operator
1.8.4. Orbital Angular Momentum
1.8.5. Ladder Operators
1.8.6. Hamiltonian

1.9. Three-Dimensional Eigenvalues and Eigenfunctions

1.9.1. Position Operator
1.9.2. Linear Momentum Operator
1.9.3. Orbital Angular Momentum and Spherical Harmonics Operator
1.9.4. Angular Equation

1.10. Three-Dimensional Potential Barriers

1.10.1. Free Particle
1.10.2. Particle in a Box
1.10.3. Central Potentials and Radial Equations
1.10.4. Infinite Spheric Well
1.10.5. Hydrogen Atom
1.10.6. 3D Harmonic Oscillator

Module 2. Quantum Physics II

2.1. Descriptions of Quantum Mechanics: Images or Representations

2.1.1. Schrödinger Picture
2.1.2. Heisenberg Picture
2.1.3. Dirac Picture or Interaction Picture
2.1.4. Change of Pictures

2.2. 3D Harmonic Oscillator

2.2.1. Creation and annihilation operators
2.2.2. Wave Functions of Fock States
2.2.3. Coherent States
2.2.4. States of Minimum Indeterminacy
2.2.5. Squeezed States

2.3. Angular Momentum

2.3.1. Rotations
2.3.2. Switches of Angular Momentum
2.3.3. Angular Momentum Basis
2.3.4. Scale Operators
2.3.5. Matrix Representation
2.3.6. Intrinsic Angular Momentum: The Spin
2.3.7. Spin Cases 1/ 2, 1, 3/ 2

2.4. Multi-Component Wave Functions: Spinorials

2.4.1. Single-Component Wave Functions: Spin
2.4.2. Two-Component Wave Functions: 1/2 Spin
2.4.3. Expected Value of Spin Observable
2.4.4. Atomic States
2.4.5. Addition of Angular Momentum
2.4.6. Clebsch-Gordan Coefficient

2.5. State of the Compound Systems

2.5.1. Distinguishable Particles
2.5.2. Indistinguishable Particles
2.5.3. Photon case: semitransparent mirror experiment
2.5.4. Quantum Bonding
2.5.5. Bell Inequalities
2.5.6. EPR Paradox
2.5.7. Bell Theorem

2.6. Introduction to Approximate Methods: Variational Method

2.6.1. Introduction to the Variational Method
2.6.2. Linear Variations
2.6.3. Rayleigh-Ritz Variational Method
2.6.4. Harmonic Oscillator: A Study by Variational Methods

2.7. Study of Atomic Models with the Variational Method

2.7.1. Hydrogen Atom
2.7.2. Helium Atom
2.7.3. Ionized Hydrogen Molecule
2.7.4. Discrete Symmetries

2.7.4.1. Parity
2.7.4.2. Temporary Inversion

2.8. Introduction to Disturbance Theory

2.8.1. Time-Independent Perturbations
2.8.2. Non-Degenerate Case
2.8.3. Degenerate Case
2.8.4. Fine Structure of Hydrogen Atom
2.8.5. Zeeman Effect
2.8.6. Coupling Constant between Spins. Hyperfine Structure
2.8.7. Time-Dependent Perturbation Theory

2.8.7.1. Two-Level Atom
2.8.7.2. Sinusoidal Perturbation

2.9. Adiabatic Approximation

2.9.1. Introduction to Adiabatic Approximation
2.9.2. The Adiabatic Theorem
2.9.3. Berry Phase
2.9.4. Aharonov-Bohm Effect

2.10. Wentzel-Kramers-Brillouin (WKB) Approximation

2.10.1. Introduction to the WKB Method
2.10.2. Classical Region
2.10.3. Tunnel Effect
2.10.4. Connection Formulas

A 100% online program that will teach you the adiabatic approach and the Aharonov-Bohm effect"