We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved de...We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.展开更多
We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<sp...We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.展开更多
We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><...We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><i><i><sub><span style="font-family:Verdana;">n</span></sub></i><span style="font-family:Verdana;"></span></i>, and the momentum eigenstates for the space-like Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.展开更多
In this paper,I criticize Joel Feinberg's argument of soft paternalism,which stands against hard paternalism,as being untenable.As assessing one's voluntariness is very difficult and controversial,paternalisti...In this paper,I criticize Joel Feinberg's argument of soft paternalism,which stands against hard paternalism,as being untenable.As assessing one's voluntariness is very difficult and controversial,paternalistic measures would be preferable to be implemented by hard paternalism rather than soft paternalism.I then examine four usual criticisms of hard paternalism from the perspective of utilitarianism and the principle of autonomy.I argue that these criticisms are unsound and unfounded,and I defend hard paternalism from the perspective of Confucian familism.I argue that as one's life and identity are inseparable from one's family,“self-regarding”actions,traditionally understood,do not only affect the self,but also one's family members.Thus,paternalistic measures to protect individuals from self-harming are also aimed to protect their family members which are indeed compatible with Mill's harm principle.展开更多
文摘We obtain the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.
文摘We obtain an approximate value of the quantized momentum eigenvalues, <em>P<sub>n</sub></em>, together with the space-like coherent eigenvectors for the space-like counterpart of the Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.
文摘We obtain the quantized momentum eigenvalues, <i><i><span style="font-family:Verdana;">P</span></i><span style="font-family:Verdana;"></span></i><i><i><sub><span style="font-family:Verdana;">n</span></sub></i><span style="font-family:Verdana;"></span></i>, and the momentum eigenstates for the space-like Schr<span style="white-space:nowrap;">ö</span>dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.
基金Funding My work on this article is partially supported by a grant[SSHD 2023-299(D)]from the College of Professional and Continuing Education,an afiliate of The Hong Kong Polytechnic University.
文摘In this paper,I criticize Joel Feinberg's argument of soft paternalism,which stands against hard paternalism,as being untenable.As assessing one's voluntariness is very difficult and controversial,paternalistic measures would be preferable to be implemented by hard paternalism rather than soft paternalism.I then examine four usual criticisms of hard paternalism from the perspective of utilitarianism and the principle of autonomy.I argue that these criticisms are unsound and unfounded,and I defend hard paternalism from the perspective of Confucian familism.I argue that as one's life and identity are inseparable from one's family,“self-regarding”actions,traditionally understood,do not only affect the self,but also one's family members.Thus,paternalistic measures to protect individuals from self-harming are also aimed to protect their family members which are indeed compatible with Mill's harm principle.
