QM 2 : Mathematical Foundations and Postulates

+Mathematical Foundations and Postulates

+You will already have seen the basic postulates in quantum mechanics in prior courses, as they emerge one-by-one in the context of wave mechanics – usually only after a lot of work first justifying and then solving the wave equation form of Schrodinger's equation. Although there is value in this approach as an introduction, it can obscure what are the essential features of quantum mechanics. 

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+In this first module, we present the postulates of quantum mechanics in a more abstract form, free from its wave-mechanics trappings, making use of linear-algebra concepts and Dirac notation. Although more abstract, this approach is more elegant and general, and hence more powerful. It is how most working physicists think and talk about quantum mechanics.

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+We begin with perhaps the simplest example that defies a classical explanation and highlights the need for a completely different description of reality: the Stern-Gerlach experiment. 

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+[S 1.1-1.5; G 3.1-3.6, 4.4; LB 2.1-2.3, 3.2, 4.1]

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+1.1. Introduction to the course. 

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+1.2 Stern-Gerlach experiment.

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+1.3 State vectors and Hilbert space.

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+1.4 Operators and matrix mechanics.

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+1.5 Superposition and measurement.

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+Abbreviations: S - Sakurai (3rd ed), LB - Le Bellac, G: Griffiths (3rd ed) 

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+Notes about the texts:

+Although we have specified one required textbook (Sakurai), we recognise that some people may prefer an alternative presentation, and so we give references to relevant sections of Griffiths and Le Bellac. See the course profile for details of these books - they are all available also online from the UQ library.

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+If you read only one bit of Sakurai, it should be chapter 1 – it contains the foundation for all that follows in this course.

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+Griffiths is a great textbook to read through, and its treatment of applications is very helpful for the later topics in this course, but for the foundational aspects (the first 3 modules), its presentation is very scattered.

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+For those who appreciate a more mathematical and structured approach, Le Bellac follows a similar 'modern approach' as Sakurai.