Non-self-adjoint operators as observables in quantum theory and nuclear physics

2010 ◽  
Vol 41 (4) ◽  
pp. 508-530 ◽  
Author(s):  
V. S. Olkhovsky ◽  
S. P. Maydanyuk ◽  
E. Recami
Keyword(s):  
Quantum Theory ◽  
Nuclear Physics ◽  
Adjoint Operators

scholarly journals Посвящается памяти выдающегося физика и математика --- Фаддеева Людвига Дмитриевича Применение квантовой теории рассеяния для расчетов простейших химических реакций --- диссоциативного прилипания, диссоциации и рекомбинации

2019 ◽  
Vol 89 (6) ◽  
pp. 803
Author(s):  
С.А. Позднеев
Keyword(s):  
Quantum Theory ◽  
Nuclear Physics ◽  
Scattering States

The quantum theory of few-body scattering based on the Faddeev-Yakubovsky equations is applied to the calculation of the main characteristics of different processes in laser, atomic, chemical and nuclear physics such as: the electron and atoms scattering with the diatomic initial rovibrational exiting molecules % $H_2$, $HD$, $D_2$, $N_2$, $Li_2$, $Na_2$, $HCl$, $HBr$ , simulation of bound and scattering states for nuclear physics %neutron-deuton, proton-deuton, positronium ion and so on. The results of this calculations are compared with available exsperimental data and other calculation.

scholarly journals Bounds on the power of proofs and advice in general physical theories

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160076 ◽  
Author(s):  
Ciarán M. Lee ◽  
Matty J. Hoban
Keyword(s):  
Quantum Theory ◽  
Quantum Structure ◽  
Interactive Proof ◽  
Interactive Proof Systems ◽  
Proof Systems ◽  
Local Measurements ◽  
General Physical ◽  
Adjoint Operators ◽  
Physical Features ◽  
Physical Principles

Quantum theory presents us with the tools for computational and communication advantages over classical theory. One approach to uncovering the source of these advantages is to determine how computation and communication power vary as quantum theory is replaced by other operationally defined theories from a broad framework of such theories. Such investigations may reveal some of the key physical features required for powerful computation and communication. In this paper, we investigate how simple physical principles bound the power of two different computational paradigms which combine computation and communication in a non-trivial fashion: computation with advice and interactive proof systems. We show that the existence of non-trivial dynamics in a theory implies a bound on the power of computation with advice. Moreover, we provide an explicit example of a theory with no non-trivial dynamics in which the power of computation with advice is unbounded. Finally, we show that the power of simple interactive proof systems in theories where local measurements suffice for tomography is non-trivially bounded. This result provides a proof that Q M A is contained in P P , which does not make use of any uniquely quantum structure—such as the fact that observables correspond to self-adjoint operators—and thus may be of independent interest.

scholarly journals ON NON-SELF-ADJOINT OPERATORS FOR OBSERVABLES IN QUANTUM MECHANICS AND QUANTUM FIELD THEORY

2010 ◽  
Vol 25 (09) ◽  
pp. 1785-1818 ◽  
Author(s):  
ERASMO RECAMI ◽  
VLADISLAV S. OLKHOVSKY ◽  
SERGEI P. MAYDANYUK
Keyword(s):  
Quantum Mechanics ◽  
Quantum Electrodynamics ◽  
Nuclear Physics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Dissipation ◽  
Interesting Possibility ◽  
Nonrelativistic Quantum Mechanics ◽  
Adjoint Operators ◽  
Unstable States

The aim of this paper is to show the possible significance, and usefulness, of various non-self-adjoint operators for suitable Observables in nonrelativistic and relativistic quantum mechanics, and in quantum electrodynamics. More specifically, this work deals with: (i) the maximal Hermitian (but not self-adjoint) time operator in nonrelativistic quantum mechanics and in quantum electrodynamics; (ii) the problem of the four-position and four-momentum operators, each one with its Hermitian and anti-Hermitian parts, for relativistic spin-zero particles. Afterwards, other physically important applications of non-self-adjoint (and even non-Hermitian) operators are discussed: in particular, (iii) we reanalyze in detail the interesting possibility of associating quasi-Hermitian Hamiltonians with (decaying) unstable states in nuclear physics. Finally, we briefly mention the cases of quantum dissipation, as well as of the nuclear optical potential.

HANS BETHE'S CONTRIBUTIONS TO SOLID-STATE PHYSICS

2006 ◽  
Vol 20 (16) ◽  
pp. 2227-2236 ◽  
Author(s):  
N. DAVID MERMIN ◽  
NEIL W. ASHCROFT
Keyword(s):  
State Physics ◽  
Quantum Theory ◽  
Solid State ◽  
Nuclear Physics ◽  
Solid State Physics ◽  
Main Interest ◽  
Doctoral Research ◽  
The Subject

Hans Bethe's doctoral research was primarily in solid-state physics. During the late 1920's and early 1930's he played a major role in developing the new quantum theory of solids. Though nuclear physics became his main interest in the mid 1930's, he continued to write papers in solid-state physics into the late 1940's, and remained interested in the subject all his life.

scholarly journals An operational construction of the sum of two non-commuting observables in quantum theory and related constructions

2020 ◽  
Vol 110 (12) ◽  
pp. 3197-3242
Author(s):  
Nicolò Drago ◽  
Sonia Mazzucchi ◽  
Valter Moretti
Keyword(s):  
Quantum Theory ◽  
Space Structure ◽  
Measuring Instruments ◽  
Spectral Measures ◽  
Feynman Path ◽  
Operational Interpretation ◽  
Real Linear ◽  
Adjoint Operators ◽  
Class Of Functions ◽  
Incompatible Observables

AbstractThe existence of a real linear space structure on the set of observables of a quantum system—i.e., the requirement that the linear combination of two generally non-commuting observables A, B is an observable as well—is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable of the form $$aA+bB$$ a A + b B ($$a,b\in {{\mathbb {R}}}$$ a , b ∈ R ) if such measuring instruments are given for the addends observables A and B when they are incompatible observables. A mathematical version of this dilemma is how to construct the spectral measure of $$f(aA+bB)$$ f ( a A + b B ) out of the spectral measures of A and B. We present such a construction with a formula which is valid for general unbounded self-adjoint operators A and B, whose spectral measures may not commute, and a wide class of functions $$f: {{\mathbb {R}}}\rightarrow {{\mathbb {C}}}$$ f : R → C . In the bounded case, we prove that the Jordan product of A and B (and suitably symmetrized polynomials of A and B) can be constructed with the same procedure out of the spectral measures of A and B. The formula turns out to have an interesting operational interpretation and, in particular cases, a nice interplay with the theory of Feynman path integration and the Feynman–Kac formula.

The characterization of quantum-mechanical operators

1950 ◽  
Vol 46 (4) ◽  
pp. 614-619 ◽  
Author(s):  
J. L. B. Cooper
Keyword(s):  
Quantum Theory ◽  
Representation Theorem ◽  
Mathematical Theory ◽  
Physical Significance ◽  
The Self ◽  
Quantum Mechanical ◽  
Resolution Of The Identity ◽  
Adjoint Operators

It is well known that the operators mainly employed in quantum theory are hermitian; it is less well known amongst physicists that they are required, in addition, to be self-adjoint. This is essential for the validity of the result known in quantum theory as the representation theorem and in the mathematical theory as the resolution of the identity. The purpose of this paper is to show that the self-adjoint operators can be characterized by a condition which is nearer to having a physical significance than those given in the literature.

scholarly journals Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

10.14311/1195 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
M. Znojil
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Hilbert Spaces ◽  
Nuclear Physics ◽  
Bound State ◽  
Wave Functions ◽  
Time Dependent ◽  
Moving Frame ◽  
Standard Textbook ◽  
Space Formulation

A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian”) Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models) is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S) of the standard physical Hilbert space of wave functions.

Rutherford and Bohr

1988 ◽  
Vol 42 (2) ◽  
pp. 229-241 ◽  
Keyword(s):  
Quantum Theory ◽  
Nuclear Physics ◽  
Body Problem ◽  
Present Knowledge ◽  
Niels Bohr ◽  
Primary Interest ◽  
Two Body Problem ◽  
Old Quantum Theory ◽  
Great Physicist ◽  
Structure Of Matter

As every physicist knows, our present knowledge of the structure of matter, of atoms and nuclei, is built on the foundations laid by Rutherford and Niels Bohr early this century. Each of them was a great physicist in his own right, but their contributions to physics, particularly in the important period from 1912 to, perhaps, 1920 owe much to their mutual interaction; we are dealing with a ‘two-body problem,’ to use current jargon. Later their paths separated: Rutherford’s primary interest was the atomic nucleus, and once he had identified its role he left the further exploration of the atom to others, whereas Bohr concentrated on the theory of the atom, and for its study developed the quantum theory. This was the ‘old’ quantum theory, spectacularly successful in explaining the hydrogen spectrum but lacking logical consistency in mixing classical and quantum concepts. He maintained an interest in the nucleus but made major contributions to nuclear physics only from 1936 on.

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