--- title: Quantum Mechanics description: Quantum mechanics is the study of physical phenomena at the atomic and subatomic scales. Learners will understand wave-particle duality, the Schrödinger equation, quantum states, and how to calculate probabilities for physical observables. category: mathematics subcategory: mathematical-physics difficulty: beginner, intermediate, advanced url: /subject/quantum-mechanics --- # Quantum Mechanics Quantum mechanics is the study of physical phenomena at the atomic and subatomic scales. Learners will understand wave-particle duality, the Schrödinger equation, quantum states, and how to calculate probabilities for physical observables. ## Available Resources 3 Books • 8 Courses • 1 Websites ## Courses ### 1. Quantum Physics III (MIT 8.06) **Author:** Barton Zwiebach Continues 8.05 with model systems of contemporary physics: perturbation theory, fine structure of hydrogen, two-dimensional electron systems, WKB approximation, lasers and particle scattering. 100 lecture videos, lecture notes, problem sets and projects equip learners to apply approximation methods to real quantum systems. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-06-quantum-physics-iii-spring-2018/ **Tags:** perturbation-theory, scattering-theory, wkb-approximation, hydrogen-fine-structure, time-dependent-perturbation ### 2. Quantum Physics II (MIT 8.05) **Author:** Barton Zwiebach The general formalism of quantum mechanics: Dirac notation, the harmonic oscillator, three-dimensional problems, angular momentum, spin, and addition of angular momentum. 26 lecture videos, detailed lecture notes that became Zwiebach's Mastering Quantum Mechanics, problem sets and exams. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-05-quantum-physics-ii-fall-2013/ **Tags:** dirac-notation, harmonic-oscillator, angular-momentum, spin, addition-of-angular-momentum ### 3. Quantum Mechanics Learn quantum mechanics from Cambridge's David Tong! Explore fundamental principles and key concepts in this comprehensive course. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.damtp.cam.ac.uk/user/tong/quantum.html **Tags:** quantum-mechanics, lecture-notes, theoretical-physics, cambridge ### 4. Quantum Physics I (MIT 8.04) **Author:** Allan Adams, Matthew Evans, Barton Zwiebach The experimental basis of quantum physics, wave mechanics, and the Schrödinger equation in one and three dimensions. 24 lecture videos, lecture notes, exams, and problem sets with solutions prepare learners to solve standard quantum systems and continue to 8.05. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-04-quantum-physics-i-spring-2013/ **Tags:** quantum-mechanics, wave-mechanics, schrodinger-equation, wavefunctions, uncertainty-principle ### 5. Introduction to Modeling and Simulation (MIT 3.021J) **Author:** Markus Buehler, Jeffrey Grossman Introduces continuum methods, atomistic and molecular simulation, and quantum mechanical modeling applied to engineering and materials problems, using web-based simulation tools rather than heavy programming. Includes 11 lecture videos, lecture slides and problem sets for hands-on practice with each method. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/3-021j-introduction-to-modeling-and-simulation-spring-2012/ **Tags:** computational-modeling, continuum-mechanics, molecular-dynamics, atomistic-simulation, quantum-mechanics ### 6. Statistical Mechanics I: Statistical Mechanics of Particles (MIT 8.333) **Author:** Mehran Kardar A graduate treatment of thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics and identical particles. Includes 26 lecture videos, detailed lecture notes, problem sets and exams with solutions, building the tools to derive equilibrium properties of many-particle systems. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2013/ **Tags:** statistical-mechanics, statistical-ensembles, kinetic-theory, quantum-statistics, interacting-systems ### 7. Quantum Mechanics Course 2 of Statistical Thermodynamics presents an introduction to quantum mechanics at a level appropriate for those with mechanical or aerospace engineering backgrounds. Using a postulatory approach that describes the steps to follow, the Schrodinger wave equation is derived and simple solutions obtained that illustrate atomic and molecular structural behavior. More realistic behavior is also explored along with modern quantum chemistry numerical solution methods for solving the wave equation. **Difficulty:** Beginner | **Language:** English | **Duration:** Three weeks of content. Six to nine hours per week, including studying. | **Price:** Free **Link:** https://www.coursera.org/learn/quantum-mechanics **Tags:** courses, science-research, mathematical-physics ### 8. Quantum Mechanics Learn the quantum mechanics needed to prepare you for the second quantum revolution (focused on quantum sensing). We use a new way to teach quantum for undergraduates by focusing on conceptual ideas and operator manipulations. This allows us to discuss more applications to experiment usually done. You need a background in the full calculus sequence and in math methods. Freshman physics and modern physics is recommended. This course is appropriate for physicists, chemists and engineers. **Difficulty:** Beginner | **Language:** English | **Duration:** Three weeks of content. Six to nine hours per week, including studying. | **Price:** Free **Link:** https://www.edx.org/learn/quantum-physics-mechanics/georgetown-university-quantum-mechanics **Tags:** courses, science-research, mathematical-physics ## Books ### 1. Principles of Quantum Mechanics **Author:** Paul A. M. Dirac Dirac's own formulation of quantum theory, developing bra-ket notation, transformation theory, and quantization from first principles. Readers finish with the abstract operator framework that underlies modern treatments, though the notation predates current textbook conventions. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1950217132?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics ### 2. Quantum Mechanics: A Modern Development **Author:** Leslie E. Ballentine Builds quantum theory from symmetry and the statistical interpretation rather than wavefunction postulates, treating ensembles, measurement, and Bell inequalities carefully. Suits readers who already know introductory quantum mechanics and want the foundations argued rather than asserted. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/9810241054?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics ### 3. Introduction to Quantum Mechanics **Author:** David J. Griffiths, Darrell F. Schroeter The standard undergraduate text, working from the Schrödinger equation through one-dimensional potentials, angular momentum, spin, and perturbation theory. Its worked problems build the calculational fluency assumed by graduate courses; the third edition adds expanded material on quantum information. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1108791107?tag=edmonddante07-20 **Tags:** books, science-research, mathematical-physics ## Websites ### 1. Wolfram MathWorld **Author:** Eric W. Weisstein MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathworld.wolfram.com **Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/quantum-mechanics