Related papers: Establishment of the conserved operators using var…
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of…
We propose six principles as the fundamental principles of quantum mechanics: principle of space and time, Galilean principle of relativity, Hamilton's principle, wave principle, probability principle, and principle of indestructibility and…
In this paper, we will assume that the structure picture of the rotation angles will be changed according to the scale of measurement (minimum measurable angle) and if we have a device with very high accuracy (high resolution) then we can…
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
The generalized uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position…
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum…
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
Quantum mechanics is reformulated using Hartle's definition of the state of an individual physical system and a variant of von Neumann's propositional calculus. An elementary set of quantum postulates lead inductively to the familiar…
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the ``classical'' detector and the ``quantum'' system,…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the…
In this paper we investigate a quantum stochastic calculus build of creation, annihilation and number of particles operators which fulfill some deformed commutation relations. Namely, we introduce a deformation of a number of particles…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
The three major theoretical principles of quantum mechanics relevant to its interpretation are: (T1), linearity; (T2), invariance under certain groups; and (T3) the orthogonality and isolation of the different branches of the state vector.…
A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped…
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…