The Energy-Levels and Transition Probabilities for a Bounded Linear Harmonic Oscillator
نویسندگان
چکیده
منابع مشابه
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...
متن کاملWavelengths , Transition Probabilities , and Energy Levels for the Spectra of Barium „ Ba
Energy levels, with designations and uncertainties, have been compiled for the spectra of barium Z=56 ions from doubly ionized to hydrogenlike. Wavelengths with classifications, intensities, and transition probabilities are also tabulated. In addition, ground states and ionization energies are listed. For many ionization stages experimental data are available; however, for those for which only ...
متن کاملEnergy Bounds for the Spinless Salpeter Equation: Harmonic Oscillator
We study the eigenvalues En` of the Salpeter Hamiltonian H = β √ m2 + p2 +vr, v > 0, β > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula En` ≈ min r>0 { v(Pn`/r) 2 + β √ m2 + r2 } provides both upper and lower energy bounds for all the eigenvalues of the problem. PACS: 03.65.Ge, 03.65.Pm, 11.10.St En...
متن کاملEnergy Evolution in Time-Dependent Harmonic Oscillator
The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general timedependent one-dimensional harmonic oscillator, whose Newton equation q̈+ω(t)q = 0 cannot be solved in general. We follow the time-evolution of an initial e...
متن کاملComments on Vacuum Energy of Harmonic Oscillator
Unlike its classical counterpart, the ground state of a quantum harmonic oscillator yields a non-zero value which has led to a significant problem regarding the cosmological constant. We will show that since observables, including that of energy, serve as a reference frame for an observer, not only is the harmonic oscillator fluctuating at the ground level, so is the reference frame of the obse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1955
ISSN: 0033-068X
DOI: 10.1143/ptp.14.214