دانلود کتاب جبرها و توزیع‌های مکانیک کوانتومی

Both quantum mechanics and statistical mechanics share the notable property that an understanding of the theory lies rather deep, yet a mastery of the associated calculations is quite straightforward. Moreover, it is perfectly reasonable to do research in either subject without usually considering the difficult problems underlying the theory. It is unfortunate that this circumstance fosters the idea that such problems as there may be are irrelevant to anything important.
The problems we have in mind do not admit of easy solutions. A necessary prerequisite to progress is a careful and rigorous formulation. This will at least separate the essential from the inessential difficulties. It will also make it difficult to believe that there are no problems.
These notes have as their goal a mathematically precise formulation of elementary quantum mechanics, based on the considerations of the following paragraphs.
The basic observables in quantum mechanics, such as position, momentum, energy and angular momentum, are represented by unbounded linear operators on some Hilbert space. These operators can have both discrete and continuous components to their spectra, necessitating a consistent scheme to take this into account.
A consistent scheme requires, firstly, an explicit choice of domain, common to all observables. This condition follows from two considerations. One, that the observables constitute an algebra reflecting the canonical commutation relations. Two, that the measured values of any observable in any state be finite. This last requirement we term the basic measurement principle.