This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges’ (1987) nonlinear dis...This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges’ (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.展开更多
Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary x^k which is independen...Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary x^k which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special k in xk (k ≥2). In particular, we find the orthogonal relation 〈n1|n2〉 = δh1,n2 (k = 0), 〈n1[V'(x)|n2〉 = (En1-En2)^2〈n1|x|n2〉 (k = 1), En = (n|V'(x)x/2|n〉 + (n|V(x)|n〉 (k = 2) and -4En(n|x|n) ~ 〈n|V'(x)x^2|n〉 + 4〈n|V(x)x|n〉 =0 (k=3). The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.展开更多
文摘This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges’ (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
基金Supported in part by Project 20150964-SIP-IPN,COFAA-IPN,Mexico
文摘Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike (non-diagonal case) and Kramers' (diagonal case) recurrence relations for arbitrary x^k which is independent of the central potential V(x). Some significant results in diagonal case are obtained for special k in xk (k ≥2). In particular, we find the orthogonal relation 〈n1|n2〉 = δh1,n2 (k = 0), 〈n1[V'(x)|n2〉 = (En1-En2)^2〈n1|x|n2〉 (k = 1), En = (n|V'(x)x/2|n〉 + (n|V(x)|n〉 (k = 2) and -4En(n|x|n) ~ 〈n|V'(x)x^2|n〉 + 4〈n|V(x)x|n〉 =0 (k=3). The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.