Hilbert Space Theory and Applications in Basic Quantum Mechanics

نویسندگان

  • Matthew R. Gagne
  • Nilgun Sungar
چکیده

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and brieáy suggest how symmetry and representations are involved in quantum theory.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

کوانتش گرانش و بررسی هندسی مکانیک کوانتمی

  We elaborate on some recent results on a solution of the Hilbert-space problem in minisuperspace quantum cosmology and discuss the consequences of making the (geometry of the) Hilbert space of ordinary nonrelativistic quantum systems time-dependent. The latter reveals a remarkable similarity between Quantum Mechanics and General Relativity.

متن کامل

Pseudo-Hermitian Quantum Mechanics

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of t...

متن کامل

he p - th / 9 41 20 47 06 D ec 9 4 Quantum computation and complexity theory

The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed.

متن کامل

Quantum Sheaves An outline of results

In this paper we start with the development of a theory of presheaves on a lattice, in particular on the quantum lattice L(H) of closed subspaces of a complex Hilbert space H, and their associated etale spaces. Even in this early state the theory has interesting applications to the theory of operator algebras and the foundations of quantum mechanics. Among other things we can show that classica...

متن کامل

Seven Principles of Quantum Mechanics

The list of basic axioms of quantum mechanics as it was formulated by von Neumann includes only the mathematical formalism of the Hilbert space and its statistical interpretation. We point out that such an approach is too general to be considered as the foundation of quantum mechanics. In particular in this approach any finitedimensional Hilbert space describes a quantum system. Though such a t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013