That equations between half-life period and life are tried to look for is the main aim in this paper. Several curves are found here. It hopes that these curves are useful to wield its roles in current research. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and radioactivity at a certain life. Through comparing we find the radioactivity is more important than the N/N0, the radioactivity is first factor and then N/N0. It is found that N/N0 decreases with decay constant increasing and the radioactivity increases and then decreases with it increasing. It increases and then decreases if N/N0 increases. The maximum value of 1.7 nuclei of radioactivity is not so big explains no neglect is available. It is old after 0.22 years. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and decay constant with half-life period at a certain time. Through comparing we find the half-life period is more important than the decay constant, it is first factor and then decay constant. It is found that N/N0 increases with half-life period increasing and it decreases with life decreasing too. The frequency and energy decrease if D wave increases. If we activate two areas two D wave molecules will be activated. In terms of that calculating half period life will double, promoting areas for four will increase life four times. Continuous utilizing this the 0.22years half one will attain 22years. The needed one is the material whose volume is big enough to produce one. Like Copper oxidation etc. Heard can be applied to the quantum CPU. How we can calculate this material whose D wave molecule life is bigger than now is the key.
Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.---By combining F\"uchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: ${A}_{21}=\left(\frac{8\ensuremath{\pi}{\ensuremath{\nu}}^{2}}{{c}^{2}{N}_{1}}\right)\left(\frac{{p}_{1}}{{p}_{2}}\right)\ensuremath{\int}{0}^{\ensuremath{\infty}}\ensuremath{\alpha}d\ensuremath{\nu}$ where
A21 is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, $\ensuremath{\nu}$ is the frequency of the light emitted in such a jump,
p1 and
p2 are the a priori probabilities of quantum states 1 and 2, and $\ensuremath{\alpha}$ is the absorption coefficient of the substance measured under conditions such that
N1 is the number of molecules per unit volume in the lower quantum state 1. The integral $\ensuremath{\int}\ensuremath{\alpha}d\ensuremath{\nu}$ is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life $\ensuremath{\tau}$ of molecules which decay from state 2 to state 1 is the reciprocal of
A21. Values of
A21 and $\ensuremath{\tau}$ are calculated from existing data for the mercury line $\ensuremath{\lambda}2537$, for a number of lines belonging to the alkali doublets, for the iodine line $\ensuremath{\lambda}5461$, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn.The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to ${10}^{\ensuremath{-}8}$ seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets $1s\ensuremath{-}m{p}_{1}$ and $1s\ensuremath{-}m{p}_{2}$ indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given
mp1 state is
m times as great as from the corresponding
mp2 state (already stated in another form by F\"uchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation.Finally the possibility and method of calculating absolute values of
A21 from the Bohr correspondence principle is indicated.
The well-known narrowing of the Mössbaur γ-line with increasing age of the excited energy state ℏω0 of the emitter nucleus (the half-life is T1/2) and broadening of the γ-line with decreasing irradiation time of the absorber nucleus are analyzed. Taking into account the short time of emission of quantum transition energy – much less than T1/2, which can be seen, for example, from the duration of the γ-signal on the scintillator, the analysis leads to the idea of the structure of the γ-quantum (photon) as an electromagnetic wave of frequency ω0 that does not carry energy (0-wave), which is emitted by the nucleus from the moment of formation of the excited state to the quantum transition, with the energy quantum ℏω0 in the form of a short-term singularity on the “tail” of this 0-wave. A possible source of 0-waves can be virtual transitions of the nucleus from the excited state to the ground state and back before the emission of an energy quantum. Detection of 0-waves is possible due to changing the width of the γ‑line with additional irradiation of the absorber nuclei by resonant 0-waves. The possibility of predicting the future decay of an excited state by 0-waves detecting and the prospects of using 0-waves for information transmission are noted. The principle of a 0-wave generator without energy radiation is proposed.
The characteristic short-time behavior of the survival probability of a decaying state, which underlies the quantum Zeno effect (QZE), is shown to follow quite simply from the Schr\"odinger equation even when the spectrum of the Hamiltonian has no finite lower bound, provided the mean energy of the initial state is finite. The failure of the Breit-Wigner form of energy distribution to predict QZE is traced to the nonexistence of a well-defined mean energy. On the basis of a suitably modified distribution, it is explicitly demonstrated that the existence of a finite lower bound to the energy distribution only affects the asymptotic decay law. For short times, the survival probability depends quadratically on time if the variance of the distribution is also finite, not otherwise. For a sufficiently well-behaved energy distribution, the asymptotic decay must be as ${t}^{{\ensuremath{-}}^{n}}$ if the spectrum has a finite lower bound, or faster than any inverse power of t if there is no lower bound.
According to theories of classical physics, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by transition coefficient. Correct calculation of this coefficient is particularly important because extremely sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient was generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In the previous papers, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results were applied to calculate the half-life values of the nuclei that emit alpha particle. In this article, the half-life calculation formulas obtained in previous studies were made simpler. It has been shown that it is applicable to all radioactive decays (alpha, beta, gamma etc.). The half-life values obtained from our calculations have been compared with the experimental values, and it has been found that the new half-life values are exactly consistent with the experimental values.
Abstract The tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier is studied. For barriers fluctuating randomly in time we show by exact numerical calculation the significant effect of barrier fluctuation on the tunneling behavior of the particle. At nonzero temperatures the computed tunneling rate constant passes through a maximum when plotted against fluctuation frequency. The resonant frequency (at which the maximum appears) slowly decreases with increase in temperature and attains a constant value at higher temperature and it increases linearly with increase in barrier height of the potential. Another important observation is that in presence of barrier fluctuation the dependence of tunneling rate constant on temperature is strongly guided by the barrier fluctuation frequency. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 280–285, 2003