This paper took the one-dimensional harmonic oscillator as the object of study,discussed the evolution of the initial state of one-dimensional oscillator with time,adopted the common precise solution and developed the approximate solution.At last,this paper compared the results of the two methods and came to the conclusion that the results were consistent,which provided a new scheme for dealing with the evolution problem of deterministic Hamiltonian system.

Quantum game is one of the important branches in quantum information.Based on the theory of the single-coin-tossing quantum game,quantum game of the same color cards is discussed here,and the theory is also extended for the model which has N states.In classical game,two players shuffle the 13 cards which have the same color in turn,and anyone can not control what the last card is.In quantum game,if one of the players,such as Bob,shuffles the cards using quantum strategies instead of classical ones,while the other player still adopts the usual classical operation,he can always make the last card be what he wants.And then,it is concluded that quantum strategies are more successful than classical ones for the game of the same color cards.

This article discusses the interaction energy of the electric dipole that consisted of positive and negative ions.Using the method of Taylor expansion,give the electric dipole's approximation potential energy.Based on the motion rules of free electric dipole,analyze the electric dipole's motion rules and solve its dynamics equation by Newton's laws of motion in the external magnetic field.Finally,conclude the electric dipole's motion rules in the external magnetic field,that is to say,the electric dipole respectively does circular motion in radial of the eternal magnetic field,and does the simple harmonic oscillattion in tangential,whose overall trajectory is irregular spiral movement.

Discuss the motion of the electric dipole in a uniform electric field, obtain the interaction force between the two particles, and get the kinetic equation by Newton's laws of motion. Finally, derive the law of motion of the electric dipole in the uniform electric field, namely : In the direction of axes, the motion of electric dipole is super- position of uniform motion in a straight line and simple harmonic motion, at the moment of couple the trajectory is periodic spiral.

Quantum information transfer is one of the important branches in quantum infromation.Based on the single state quantum information transfer in spin chain,the transfer of two and three states information in spin chain are discussed in detail,and then the scheme is expanded to the arbitrary n states furthermore. Finally,the probability formula of the quantum information of the arbitrary n-state transfers in spin chain is obtained,and the condition that the arbitrary n-state information can be transferred perfectly in spin chain is given as well.Accordingly,a reasonable theoretical scheme is offered for the perfect transfer of the arbitrary n-state information.

The interaction energy of free dipole made up of positive and negative ions is discussed,and the motions of the dipole with this forces acting on it are analyzed.After solved the motion equations,we find the motion of the free dipole is the superposition of uniform rectilinear translation and simple harmonic motion.And its mass center makes uniform rectilinear translation.In mass center coordinate,the ions make the simple harmonic motion near their equilibrium positions.

Based on the quantum game theory of a single coin,a kind of method is given on how to discuss quantum game of two discriminable coins.That is,the quantum game of two coins can be considered as linear superimposition of single-coin quantum game.And it is concluded that for the two discriminable coins quantum strategies are also successful than classical ones and the player who adopts quantum strategies could always control the game.

Recently, some schemes on how to realize quantum NOT gate have been reported. In this paper, we theoretically propose a new scheme by means of quantum theory. Here we use a quantum coin as a quantum NOT gate and its logic function is realized by the quantum game theory. In our schemes, classical noise does not disturb the realization of quantum NOT gate.