Gin-yih Tsaur and Jyhpyng Wang
European Journal of Physics 35, 015006 (2014)
Solvable models of the Schroedinger equation are important models of quantum systems because they are idealistic approximations of real quantum systems and much insight into real quantum systems can be gained from the exact solutions of the solvable models. In this paper we show that a universal Laplace transform scheme can be used to solve the Schroedinger equations in closed form for all known solvable models. The work demonstrates how to apply the Laplace transform to differential equations with non-constant coefficients, which is useful in many branches of physics in addition to quantum mechanics. The advantages of the Laplace transform over the power expansion method and its connection with the methods of supersymmetry shape-invariant potentials and quantum canonical transformation, which also give closed-form solutions for solvable models, are elucidated.
Tung-Chang Liu, Xi Shao, Chuan-Sheng Liu, Minqing He, Bengt Eliasson, Vipin Tripathi, Jao-Jang Su, Jyhpyng Wang, and Shih-Hung Chen
New Journal of Physics 15, 025026 (2013)
We study theoretically and numerically the acceleration of protons by a combination of laser radiation pressure acceleration and Coulomb repulsion of carbon ions in a multi-ion thin foil made of carbon and hydrogen. The carbon layer helps to delay the proton layer from disruption due to the Rayleigh–Taylor instability, to maintain the quasi-monoenergetic proton layer and to accelerate it by the electron-shielded Coulomb repulsion for much longer duration than the acceleration time using single-ion hydrogen foils. Particle-in-cell simulations with a normalized peak laser amplitude of a0=5 show a resulting quasimonoenergetic proton energy of about 70 MeV with the foil made of 90% carbon and 10% hydrogen, in contrast to 10 MeV using a single-ion hydrogen foil.
G. Tsaur, N.-H. Kang, Z.-H. Xie, S.-H. Chen, and J. Wang
Physical Review A 83, 033801 (2011)
Field-induced birefringence, also known as cross-polarization wave generation, has played an important role in ultrafast nonlinear optics. In this paper we analyze birefringence induced by relativistic collective motion of electrons driven by a high-intensity laser field. An analytical expression for the phase difference between the parallel and perpendicular polarizations of a weak probe pulse with respect to the polarization of a strong pump pulse as a function of intensity, density, and wavelengths is derived. It is shown that under typical experimental conditions of high-field physics, the effect is well above detection threshold. The analysis is compared with particle-in-cell simulations, and the agreement provides good support for the theory.
C.-H. Pai, Y.-Y. Chang, L.-C. Ha, Z.-H. Xie, M.-W. Lin, J.-M. Lin, Y.-M. Chen, G. Tsaur, H.-H. Chu, S.-H. Chen, J.-Y. Lin, J. Wang, and S.-Y. Chen
Physical Review A 82, 063804 (2010)
As an intense laser pulse propagates through an underdense plasma, the strong ponderomotive force pushes away the electrons and produces a trailing plasma bubble. In the meantime the pulse itself undergoes extreme nonlinear evolution that results in strong spectral broadening toward the long-wavelength side. By experiment we demonstrate that this process can be utilized to generate ultrashort midinfrared pulses with an energy three orders of magnitude larger than that produced by crystal-based nonlinear optics. The infrared pulse is encapsulated in the bubble before exiting the plasma, hence is not absorbed by the plasma. The process is analyzed experimentally with laser-plasma tomographicmeasurements and numerically with three-dimensional particle-in-cell simulation. Good agreement is found between theoretical estimation, numerical simulation, and experimental results.
Gin-yih Tsaur and Jyhpyng Wang
Physical Review A 65, 012104 (2001)
Owing to the operator nature of the quantum dynamical variables, classical canonical transformations for integrating the equations of motion cannot be extended to the quantum domain. In this paper, a general procedure is developed to construct the sequences of quantum canonical transformations for integrating the Schroedinger equations. The sequence is made of three elementary canonical transformations that constitute a much larger class than the unitary transformations. In conjunction with the procedure, we also developed a factorization technique that is analogous to the method of integration factor in classical integration. For demonstration, with the same procedure we integrate nine nontrivial models, including the centripetal barrier potential, the Kratzer’s molecular potential, the Morse potential, the Poeschl-Teller potential, the Hulthe´n potential, etc.
M.-C. Chou, P.-H. Lin, C.-A. Lin, J.-Y. Lin, J. Wang, and S.-Y. Chen
Physical Review Letters 99, 063904 (2007)
Dramatic enhancement of optical field-ionization collisional-excitation x-ray lasing is achieved by using an optically-preformed plasma waveguide. With a 9-mm-long pure krypton plasma waveguide prepared by using the axicon-ignitor-heater scheme, lasing at 32.8 nm is enhanced by 400 folds relative to the case without the plasma waveguide. An output level of 8 x 1010 photon/shot is reached at an energy conversion efficiency of 2 x 10-6. The same method is used to achieve x-ray lasing in a gas jet for the high-threshold low-gain transition at 46.9 nm in neon-like argon.