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21.
From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the
absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest,
one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the
particle at rest, and the resulting de Broglie matter wave length, λD, of the particle with kinetic energy of motion of mv2/2. The relationship so deduced, λD∝√λ, suggests that visible wavelengths of light, from about 4000 ?, in the violet, to beyond about 7000 ?, in the red, on
absorption by an electron at rest, lead to material electron wavelengths, λD, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing
organisms, at about a size of 50–100 ?. In addition to understanding the mechanism of photosynthesis as a material wave mediated
phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain
a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties
of material waves, and to precisely control their properties for applications including lithography. 相似文献
22.
We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 相似文献
23.
We study perturbations of the quantized version
0 of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of
0 are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf 相似文献
24.
John R. Klauder 《Entropy (Basel, Switzerland)》2022,24(10)
Canonical quantization has created many valid quantizations that require infinite-line coordinate variables. However, the half-harmonic oscillator, which is limited to the positive coordinate half, cannot receive a valid canonical quantization because of the reduced coordinate space. Instead, affine quantization, which is a new quantization procedure, has been deliberately designed to handle the quantization of problems with reduced coordinate spaces. Following examples of what affine quantization is, and what it can offer, a remarkably straightforward quantization of Einstein’s gravity is attained, in which a proper treatment of the positive definite metric field of gravity has been secured. 相似文献
25.
26.
The quantum dynamics of carriers bound to helical tube surfaces is investigated in a thin-layer quantization scheme. By numerically solving the open-boundary Schrödinger equation in curvilinear coordinates, geometric effect on the coherent transmission spectra is analysed in the case of single propagating mode as well as multimode. It is shown that, the coiling endows the helical nanotube with different transport properties from a bent cylindrical surface. Fano resonance appears as a purely geometric effect in the conductance, the corresponding energy of quasibound state is obviously influenced by the torsion and length of the nanotube. We also find new plateaus in the conductance. The transport of double-degenerate mode in this geometry is reminiscent of the Zeeman coupling between the magnetic field and spin angular momentum in quasi-one-dimensional structure. 相似文献
27.
In this paper, a modified single-index signal regression (mSISR) method is proposed to construct a nonlinear and practical model with high-accuracy. The mSISR method defines the optimal penalty tuning parameter in P-spline signal regression (PSR) as initial tuning parameter and chooses the number of cycles based on minimizing root mean squared error of cross-validation (RMSECV). mSISR is superior to single-index signal regression (SISR) in terms of accuracy, computation time and convergency. And it can provide the character of the non-linearity between spectra and responses in a more precise manner than SISR. Two spectra data sets from basic research experiments, including plant chlorophyll nondestructive measurement and human blood glucose noninvasive measurement, are employed to illustrate the advantages of mSISR. The results indicate that the mSISR method (i) obtains the smooth and helpful regression coefficient vector, (ii) explicitly exhibits the type and amount of the non-linearity, (iii) can take advantage of nonlinear features of the signals to improve prediction performance and (iv) has distinct adaptability for the complex spectra model by comparing with other calibration methods. It is validated that mSISR is a promising nonlinear modeling strategy for multivariate calibration. 相似文献
28.
Replacing vector type of interaction of the Thirring–Wess model by the chiral type a new model is presented which is termed here as chiral Thirring–Wess model. Ambiguity parameters of regularization are so chosen that the model falls into the Faddeevian class. The resulting Faddeevian class of model in general does not possess Lorentz invariance. However we can exploit the arbitrariness admissible in the ambiguity parameters to relate the quantum mechanically generated ambiguity parameters with the classical parameter involved in the masslike term of the gauge field which helps to maintain physical Lorentz invariance instead of the absence of manifestly Lorentz covariance of the model. The phase space structure and the theoretical spectrum of this class of model have been determined through Dirac’s method of quantization of constraint system. 相似文献
29.
安博 《原子与分子物理学报》2015,32(6)
在D维空间下使用完全量子化规则计算了具有离心项的Woods-Saxon势,根据动量积分 (其中 )和Pekeris近似化条件,得到了系统的任意l波Schrödinger方程的解和能谱方程.讨论了束缚态能谱的有关性质. 相似文献
30.