Is the Heisenberg picture better than the Schrödinger picture?

1966 ◽  
Vol 44 (4) ◽  
pp. 871-877 ◽  
Author(s):  
A. Katz
Keyword(s):  
Heisenberg Picture ◽  
Schrödinger Picture ◽  
Better Than

QUANTUM RADIATIVE PROPERTIES OF THE CRYSTAL-LIKE GAS

2001 ◽  
Vol 15 (01) ◽  
pp. 71-74
Author(s):  
C. F. LO ◽  
L. H. YUNG
Keyword(s):  
Radiative Properties ◽  
Heisenberg Picture ◽  
Quantum Properties ◽  
Previous Claim ◽  
Schrödinger Picture

In this paper we have examined the quantum properties of the radiance of the crystal-like gas (CLG) in both the Schrödinger picture and Heisenberg picture. We have found that the previous claim of L. M. Duan and G. C. Guo [Quantum Semiclass. Opt.9, 45 (1997)] that the CLG can radiate light with the intensity increasing with time exponentially is in fact erroneous.

scholarly journals Everettian relative states in the Heisenberg picture

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200783
Author(s):  
Samuel Kuypers ◽  
David Deutsch
Keyword(s):  
Quantum Theory ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
Technical Problems ◽  
Heisenberg Picture ◽  
State Construction ◽  
The Many ◽  
Definition Of ◽  
Schrödinger Picture ◽  
Relative States

Everett's relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently approximative nature and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian , we are referring not only to Everett's own work, but also to versions of quantum theory that elaborate and refine his. The notion of relative states first appeared in Everett (Everett 1973 In The many worlds interpretation of quantum mechanics (eds BS DeWitt, N Graham)). We are proposing a formalism for relative states that is more detailed and more illuminating than Everett's.) Our construction also allows us to give a more precise definition of an Everett ‘universe’, under which it is fully quantum, not quasi-classical, and we compare the Everettian decomposition of a quantum state with the foliation of a space–time.

scholarly journals A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture

2018 ◽  
Vol 33 (20) ◽  
pp. 1850122 ◽  
Author(s):  
F. M. Ciaglia ◽  
A. Ibort ◽  
G. Marmo
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Mathematical Structure ◽  
Heisenberg Picture ◽  
Schrödinger Picture

In this paper, we review Schwinger’s formulation of Quantum Mechanics and argue that the mathematical structure behind Schwinger’s “Symbolism of Atomic Measurements” is that of a groupoid. In this framework, both the Hilbert space (Schrödinger picture) and the [Formula: see text]-algebra (Heisenberg picture) of the system turn out to be derived concepts, that is, they arise from the underlying groupoid structure.

Schrödinger picture, Heisenberg picture and probabilistic aspects

2014 ◽  
pp. 94-121
Author(s):  
Giampiero Esposito ◽  
Giuseppe Marmo ◽  
Gennaro Miele ◽  
George Sudarshan
Keyword(s):  
Heisenberg Picture ◽  
Schrödinger Picture

A Note on the Equations of Motion in Non-Relativistic Quantum Mechanics

1935 ◽  
Vol 31 (2) ◽  
pp. 291-294
Author(s):  
F. C. Powell
Keyword(s):  
Dynamical System ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Equations Of Motion ◽  
Invariant Form ◽  
Relativistic Quantum Mechanics ◽  
Heisenberg Picture ◽  
Physical Consequences ◽  
Schrödinger Picture

It is well known that the motion of a dynamical system can be pictured in two distinct ways, which Dirac names the Heisenberg picture and the Schrödinger picture. The equations of motion take different forms in the two pictures, but of course have identical physical consequences, since the motion of the system does not depend in any way on which picture we choose. It should therefore be possible to express the equations in an invariant form (independent, that is, of the picture used). It will be shown in this note that not only can this be done (equation (3)), but it can be done in such a way that it is not even necessary to introduce a picture at all (equation (3′)).

Q. M. Pictures; Heisenberg Equation; Linear Response; Superoperators and Non-Markovian Equations

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Kinetic Equations ◽  
Fixed Time ◽  
Heisenberg Equation ◽  
System State ◽  
Interaction Picture ◽  
Von Neumann ◽  
Heisenberg Picture ◽  
Independent Basis ◽  
Complete Set ◽  
Schrödinger Picture

Three fundamental and equivalent mathematical frameworks (“pictures”) in which quantum theory can be lodged are exhibited and their relations and relative advantages/disadvantages are discussed: (1) The Schrödinger picture considers the dynamical development of the overall system state vector as a function of time relative to a fixed complete set of time-independent basis eigenstates; (2) The Heisenberg picture (convenient for the use of Green’s functions) embeds the dynamical development of the system in a time-dependent counter-rotation of the complete set of basis eigenstates relative to the fixed, time-independent overall system state, so that the relation of the latter fixed system state to the counter-rotating basis eigenstates is identically the same in the Heisenberg picture as it is in the Schrödinger picture; (3) the Interaction Picture addresses the situation in which a Hamiltonian, H=H0+H1, involves a part H0 whose equations are relatively easy to solve and a more complicated part, H1, treated perturbatively. The Heisenberg equation of motion for operators is discussed, and is applied to annihilation and creation operators. The S-matrix, density matrix and von Neumann equation, along with superoperators and non-Markovian kinetic equations are also addressed (e.g. the intracollisional field effect).

Hamiltonian approach to the method of summation over Feynman histories

1963 ◽  
Vol 59 (1) ◽  
pp. 147-155 ◽  
Author(s):  
H. Davies
Keyword(s):  
Variational Method ◽  
Hamiltonian Approach ◽  
Canonical Coordinates ◽  
Quantization Procedure ◽  
Heisenberg Picture ◽  
Independent Variables ◽  
Schrödinger Picture

AbstractThe Feynman method of quantization by summation over q-histories is extended to a summation over q, p-histories, corresponding to the classical variational method of treating q and p as independent variables. The equivalence of this q-p summation to the usual quantization procedure is shown in the Heisenberg picture by choosing convenient canonical coordinates and in the Schrödinger picture by obtaining the usual representations of the q, p operators.

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

Localization of immunolabels by electron microscopy and image averaging

1983 ◽  
Vol 41 ◽  
pp. 282-283
Author(s):  
J. Frank ◽  
P.-Y. Sizaret ◽  
A. Verschoor ◽  
J. Lamy
Keyword(s):  
Electron Microscopy ◽  
Single Particle ◽  
Attachment Site ◽  
Uranyl Acetate ◽  
Limulus Polyphemus ◽  
Resolution Limit ◽  
Electron Microscopic ◽  
Image Averaging ◽  
Top View ◽  
Better Than

The accuracy with which the attachment site of immunolabels bound to macromolecules may be localized in electron microscopic images can be considerably improved by using single particle averaging. The example studied in this work showed that the accuracy may be better than the resolution limit imposed by negative staining (∽2nm).The structure used for this demonstration was a halfmolecule of Limulus polyphemus (LP) hemocyanin, consisting of 24 subunits grouped into four hexamers. The top view of this structure was previously studied by image averaging and correspondence analysis. It was found to vary according to the flip or flop position of the molecule, and to the stain imbalance between diagonally opposed hexamers (“rocking effect”). These findings have recently been incorporated into a model of the full 8 × 6 molecule.LP hemocyanin contains eight different polypeptides, and antibodies specific for one, LP II, were used. Uranyl acetate was used as stain. A total of 58 molecule images (29 unlabelled, 29 labelled with antl-LPII Fab) showing the top view were digitized in the microdensitometer with a sampling distance of 50μ corresponding to 6.25nm.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

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