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Updated in [March 06th, 2023]

This course, Mastering Quantum Mechanics Part 1: Wave Mechanics, is designed to provide students with a sophisticated view of quantum mechanics and its proper mathematical foundation. It is the first module of a three-part series, and will review the basics of wave mechanics and introduce the variational principle. Students will learn about the technology of spin one-half states and spin operators, and gain an in-depth look into linear algebra to establish the mathematical foundation necessary to do quantum mechanics. The course will conclude by developing the bra-ket notation of Dirac.

To follow this course, students must have some basic familiarity with quantum mechanics, including knowledge of the Schrödinger equation and its solutions for the square well potential, the harmonic oscillator, and the hydrogen atom. Additionally, students must be proficient in calculus and have some knowledge of linear algebra.

Completing the 3-part Mastering Quantum Mechanics series will give students the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics. The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors.

Learners have found this course to be of the highest quality, with one student saying, “I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.” Another student, an engineering student from India, said, “Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable.”

This course is an excellent opportunity for students to gain a comprehensive understanding of quantum mechanics and its mathematical foundation. It is a rigorous course that will provide students with the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.

[Applications]
Upon completion of this course, learners will have a comprehensive understanding of wave mechanics and its application in quantum mechanics. They will be able to apply the variational principle to solve problems, understand the technology of spin one-half states and spin operators, and use the bra-ket notation of Dirac. Learners will be equipped with the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.

[Career Paths]
The career paths recommended to learners of this course include:

1. Quantum Computing Engineer: Quantum computing engineers are responsible for developing and maintaining quantum computing systems. They must have a deep understanding of quantum mechanics and be able to apply it to the development of new technologies. As the field of quantum computing continues to grow, the demand for quantum computing engineers is expected to increase.

2. Quantum Physicist: Quantum physicists are responsible for researching and developing theories related to quantum mechanics. They must have a deep understanding of the principles of quantum mechanics and be able to apply them to the development of new technologies. As the field of quantum physics continues to grow, the demand for quantum physicists is expected to increase.

3. Quantum Information Scientist: Quantum information scientists are responsible for researching and developing new technologies related to quantum information. They must have a deep understanding of quantum mechanics and be able to apply it to the development of new technologies. As the field of quantum information continues to grow, the demand for quantum information scientists is expected to increase.

4. Quantum Engineer: Quantum engineers are responsible for designing and developing new technologies related to quantum mechanics. They must have a deep understanding of quantum mechanics and be able to apply it to the development of new technologies. As the field of quantum engineering continues to grow, the demand for quantum engineers is expected to increase.

[Education Paths]
Recommended Degree Paths:
1. Bachelor of Science in Physics: This degree program provides students with a comprehensive understanding of the fundamental principles of physics, including mechanics, thermodynamics, electricity and magnetism, optics, and quantum mechanics. Students will also gain an understanding of the latest developments in physics research and technology.

2. Master of Science in Physics: This degree program provides students with an advanced understanding of the principles of physics, including quantum mechanics, relativity, and particle physics. Students will also gain an understanding of the latest developments in physics research and technology.

3. Doctor of Philosophy in Physics: This degree program provides students with an in-depth understanding of the principles of physics, including quantum mechanics, relativity, and particle physics. Students will also gain an understanding of the latest developments in physics research and technology.

Developing Trends:
1. Quantum Computing: Quantum computing is an emerging field of research that seeks to use the principles of quantum mechanics to create powerful computers that can solve complex problems.

2. Artificial Intelligence: Artificial intelligence is a rapidly growing field of research that seeks to use machine learning and other techniques to create intelligent systems that can solve complex problems.

3. Nanotechnology: Nanotechnology is a rapidly growing field of research that seeks to use nanoscale materials and devices to create new materials and devices with unique properties.