The procedure of transition from classical observables to quantum (operator) observables in quantum mechanics is discussed. By an example it is shown that, even in simple cases, the method of self-adjoint extensions of formal differential expressions for defining physical observables as operators is...
quantum mechanicshydrogen atomquantization rulescurved surfacesNew quantization rules for classical systems are obtained using the Titchmarsh expansion. These rules generalize the conventional ones and are reduced to them when a transition to Cartesian coordinates exists. An equation generalizing the Schr...
Sniatycki- Geometric Quantization and Quantum Mechanics- Chapter 7.2- specifically starting from equation 7.84 Or a very brief statement of resutls, without derivations in Brian Hall's book on Quantum Theory for Mathematicians chapter 23.6 equation 23.39. Share Cite Improve this answer...
When I quantize a Simple Harmonic Oscillator in Quantum Mechanics as defining a=ω2−−√q+i2ω−−−√p ,a†=ω2−−√q−i2ω−−−√pa=ω2q+i2ωp ,a†=ω2q−i2ωp And q=12ω−−−√(a+a†) ,p=−iω2−−√(a−a†)q=12ω(a...
In quantum mechanics, expectation values of an observable \(\hat{A}\) are calculated as overlap matrix elements like \(\left\langle \Psi \right|\hat{A}\left|\Psi \right\rangle\), which defines the standard scalar product in Hilbert space. However, the eigenstates of a NH Hamiltonian \...
The unsatisfactory status of the interpretation of the wave function of the Universe in canonical quantum gravity is reviewed. The ``naive interpretation''... W Unruh,R Wald - 《Physical Review D Particles & Fields》 被引量: 581发表: 1989年 Quantum mechanics of the gravitational field in asym...
摘要: The particles interchanging operator and hamiltonian for two particles on a quantum sphere are constructed. Though there is no interaction hamiltonian, "interaction energy" occurs. Itsuggests a possibility that in a future quantum theory, allparticles might be free....
Quantum circuit theory has become a powerful and indispensable tool to predict the dynamics of superconducting circuits. Surprisingly however, the question of how to properly account for a time-dependent driving via external magnetic fields has hardly be
Quantization Riemannian exponential Mechanics 0. Introduction The “factor-ordering problem” was unavoidable within the Matrix Mechanics methods. It has been kept in Quantum Mechanics textbooks as an unpleasant question ([22], p. 98), even unsolvable ([16], II, 15) and always subtle ([20], ...
Renormalization in quantum mechanicsBound state solutionWe argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann's method of self-adjoint extensions (SAE) to get this inequivalent ...