Artics | Leonard

Interest-Math (1)

classical-theory (5)

measurement (3)

quantum-computing (3)

data-science (1)

number-theory (1)

Artics

16 posts

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Prove the Irrationality of Square Root of 2

Feb 19, 2022
2 minutes read

Various methods of proving the irrationality of the square root of integer 2. Including the method by contradiction and the direct way.

Machine Learning in Quantum Mechanics, Up to 2021

Dec 12, 2021
21 minutes read

In the recent(at 2021) decades, machine learning algorithms have been popular in almost all disciplines of science and even art. People have found out that a huge share of research and production problems can be viewed as instances of basic tasks that could get well solved with the modern powerful hardware and algorithms. In physics, there has been already plenty of applications covering data manipulation and model/theory discovering. However, just like those famous algorithms in the past, machine learning has its own caveats. Researchers should get well understanding about the boundary of algorithms' ability. Being a well-trained user instead of package importer would be the new requirements of people in related fields. In this review, we will discuss the success applications of machine learning in quantum physics in recent years and the potential limitation. Then the reader could get a clearer picture on the development of machine learning and quantum physics frontier.

Time in Quantum Mechanics

Sep 25, 2021
11 minutes read

Time in quantum mechanics is always left as an parameter in the equation of motion. In the non-relativistic quantum theory we find time in the derivative of wavefunction, while in the relativistic quantum field theory, it is not at the same status of spatial position: we introduce the space-time dependent field operator only for Lorentz covariance for the equation of motion. Whether can we have an intrinsic interpretation of time flow in quantum mechanics was early discussed by Don Page and William Wootters with the purpose to match the energy superselection rule. Though it may not be a correct theory for our world or even 'close' to it, it is worthy to discuss in modern view here as a consistent approach to the time puzzle.