In this note, I've demonstrated how the mathematically rigorous treatment of observables with continuous spectra works. At the end, I've introduced a little question of mine arosed while writing this note. It was represented in the 11'th session of Quantum Theory study circle at Quanta.

This paper discusses the mathematical differences between electric and magnetic dipoles. I starts with analyzing the necessity of their difference and then discuss the possibility of considering dipoles as fundamental sources of EM fields rather than electric monopoles and currents.

P.S: In the "Final Instance" part, there is a mistake negleting the effect of bound surface-charges. applying this effect, the total magnetic field is zero everywhere which leads to the fact that if you attempt to construct this magnetization using dipoles arrangement, they all cancel eachother and produce no effective field.

This paper was my attempt to formulate the probabilistic approach to classical mechanics before I get familiar with Liouville's theory; Therefore, I used a frustrating method similar to what is used for Fokker-Planck theory. Then, I derived Liouville's equation and analyzed its solution in different situations.

This paper is my attempt to build the Schrodinger equation starting from Liouville-Von Neumann equation. This ended up with the possibility of considering the Quantum Mechanics based on density matrix rather than state vectors.

This is a paper written by Asher Peres in 1995 which investigates the necessary and sufficient conditions on generalization of Schmidt decomposition to a composite system with more than two subsystems. It turns out that it's simpler that it appears!

This is a paper written by E. T. Jaynes in 1957 which argue that statistical mechanics is not actually a "physical theory" dependent on physical phenomena (such as ergodicity, metric transitivity, etc.). In this paper, statistical mechanics is considered as "the best possible estimate we can make based on available information" as a statistical inference. If ergodicity is seen to be violated, we are given some "new information" which alters our "best possible estimate" about the system so doesn't contradict other perspectives. I personally prefer This perspective to the subject and enjoyed reading this paper.

This is a paper written by E. T. Jaynes in 1971 which demonstrates the possibility of rising the Boltzmann's H function in course of time (contrary to the H-theorem). It discusses an "Empirically Rializable" way to produce H-theorem-violating systems Using a simple beautiful method. (I have presented this paper in QSC. More info can be found here in "Historical Papers" presentations).

This is a paper written by U. Klein which tries to formulate the classical probabilistic mechanics Similar to the Quantum Theory and find the "Quantization Rule".

This paper is the original paper written by W. Heisenberg in July 1925 which is considered as the birth of Quantum Mechanics translated in English (ref: Sources of Quantum Mechanics, Van Der Wearden). There is also a paper written by M. Khorrami explaining this paper with modern notation which I've found interesting.