Theory

Quantum Mechanics in the light of spins

A theoretical toolkit for understanding spin physics and quantum information science, starting with the fundamentals of quantum mechanics and building into more complex topics.

The theory of quantum mechanics is rich in its mathematical beauty and power for describing the microscopic physical world. In these posts, we present quantum mechanics from the perspective of spins physics, utilizing the language of magnetic resonance to introduce and understand the key ideas underlying quantum information science. Beginning from the postulates of quantum mechanics, this section aims to equip the reader with the theoretical background required to understand complex concepts in magnetic resonance, quantum sensing, and quantum computing.

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Postulate VI – Time evolution (Part II)

The full scripts presented in this post are available at these links: MATLAB, Python In the previous post we saw how the time-dependent Schrödinger equation allows us to calculate how quantum mechanical systems evolve with time, under the effect of the Hamiltonian operator, which describes the total energy of the system. In the case where […]

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Postulate V: Collapse of the wave function

Collapse of the wave function. Sounds intense, in’t? What does it mean? That’s the topic of this post. When we discussed the second and third postulates of quantum mechanics, we saw that, for a given physical observable , we can only measure an eigenvalue of the operator associated with . We also saw with the […]

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Postulate II & III – Observable operators and eigenvalues

The full scripts presented in this post are available at these links: MATLAB, Python With the first postulate of quantum mechanics, we learnt that everything there is to know about a quantum system is encapsulated in the wave function . But so far, the wave function is sort of a black box and we still […]

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Postulate VI: Time evolution (Part I)

This post presents the last of the six postulates of quantum mechanics. Up to now, we have seen how a quantum mechanical state is defined, what is the outcomes of measurements on such systems, and how measurements affect them. The sixth postulate determines how quantum mechanical system evolve in time; it defines the equation of […]

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Postulate IV: Probability for a measurement

The full scripts presented in this post are available at these links: MATLAB, Python In the previous post, we saw that for any state , measuring the observable can only result in one of the eigenvalues of the Hermitian operator associated with . We concluded by asking what could be the probability of measuring one […]

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Postulate I – Describing the state of a system

The full scripts presented in this post are available at these links: MATLAB, Python To develop the framework of quantum mechanics in the early 20th century, pioneer scientists had to question our knowledge about the world. They had to ask themselves what a measurement and an observer are, and how they interact. When Newton introduced […]

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Postulates of quantum mechanics – an intro

Hi reader, welcome to this post series on the postulates of quantum mechanics!  Have you ever followed classes on quantum mechanics? A common approach to presenting this fascinating topic is to first introduce the six postulates of quantum mechanics, one by one. Here, we intend to do something similar: each of the next six posts […]

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Postulates of Quantum Mechanics

This series of posts lays out the foundational postulates of quantum mechanics using the two-level system of spin 1/2 particles as our model. In additionto a mathematical description of these postulates, MATLAB and Python code is included to show how to translate these ideas in a coding environment.

These posts will provide the mathematical foundation for more complex concepts in quantum mechanics and magnetic resonance, and the building blocks for code development of spin dynamics.
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