Dissertations / Theses on the topic 'Schr??dinger equation'
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Grice, Glenn Noel Mathematics UNSW. "Constant speed flows and the nonlinear Schr??dinger equation." Awarded by:University of New South Wales. Mathematics, 2004. http://handle.unsw.edu.au/1959.4/20509.
Full textAydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.
Full textdinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.
Mugassabi, Souad. "Schrödinger equation with periodic potentials." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/4895.
Full textKoca, Burcu. "Studies On The Perturbation Problems In Quantum Mechanics." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604930/index.pdf.
Full textodinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
Alici, Haydar. "Pseudospectral Methods For Differential Equations: Application To The Schrodingertype Eigenvalue Problems." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1086198/index.pdf.
Full textdinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then introduced to deduce the effciency of the method.
Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.
Full textdinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
Ozdemir, Sevilay. "Bose-einstein Condensation At Lower Dimensions." Master's thesis, METU, 2004. http://etd.lib.metu.edu/upload/755959/index.pdf.
Full textBucurgat, Mahmut. "Study Of One Dimensional Position Dependent Effective Mass Problem In Some Quantum Mechanical Systems." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12609405/index.pdf.
Full textdinger equation for some well known potentials, such as the deformed Hulthen, the Mie, the Kratzer, the pseudoharmonic, and the Morse potentials. Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions exactly. By introducing a free parameter in the transformation of the wave function, the position dependent effective mass problem is reduced to the solution of the Schrö
dinger equation for the constant mass case. At the same time, the deformed Hulthen potential is solved for the position dependent effective mass case by applying the method directly. The Morse potential is also solved for a mass distribution function, such that the solution can be reduced to the constant mass case.
Moşincat, Răzvan Octavian. "Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33244.
Full textDeng, Shengfu. "A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28254.
Full textPh. D.
Rust, Mike. "The Approximate Inclusion of Triple Excitations in EOM-type Quantum Chemical Methods." Scholarship @ Claremont, 2001. https://scholarship.claremont.edu/hmc_theses/135.
Full textSingh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.
Full textOliveira, Junior José Carlos de. "Equações elípticas semilineares e quasilineares com potenciais que mudam de sinal." reponame:Repositório Institucional da UnB, 2015. http://dx.doi.org/10.26512/2015.09.T.20199.
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Neste trabalho, consideramos o problema autônomo {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ em que N≥3, a função V é não periódica, radialmente simétrica e muda de sinal e a não linearidade f é assintoticamente linear. Além disso, impomos que V possui um limite positivo no infinito e que o espectro do operador L≔-∆+V tem ínfimo negativo. Sob essas condições, baseando-se em interações entre soluções transladadas do problema no infinito associado, é possível mostrar que tal problema satisfaz a geometria do teorema de linking clássico e garantir a existência de uma solução fraca não trivial. Em seguida, estabelecemos a existência de uma solução não trivial para o problema não autônomo {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ sob hipóteses similares ao problema anterior, admitindo também que f(x,u)=f(|x|,u) dentre outras condições. Aplicamos novamente o teorema de linking para garantir que tal problema possui uma solução não trivial. Por fim, provamos que o problema quasilinear {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ em que o potencial V muda de sinal, podendo ser não limitado inferiormente, e a não linearidade g(x,u), quando |x|→∞, possui um certo tipo de monotonicidade, possui uma solução não trivial. A existência de tal solução é provada por meio de uma mudança de variável que transforma o problema num problema semilinear, nos permitindo, assim, empregar o teorema do passo da montanha combinado com o lema splitting.
In this work, we consider the autonomous problem {(-∆u+V(x)u=f(u) em R^N,@u∈H^1 (R^N)\\{0},)┤ where N≥3, V is a non-periodic radially symmetric function that changes sign and the nonlinearity f is asymptotically linear. Furthermore, we impose that V has a positive limit at infinity and the spectrum of the operator L≔-∆+V has negative infimum. Under these conditions, employing interaction between translated solutions of the problem at infinity, it is possible to show that such problem satisfies the geometry of the classical linking theorem and garantee the existence of a nontrivial weak solution. After that, we establish the existence of a nontrivial weak solution for the nonautonomous problem {(-∆u+V(x)u=f(x,u) em R^N,@u∈H^1 (R^N)\\{0},)┤ under similar hyphoteses to the previous problem, assuming also that f(x,u)=f(|x|,u) among others conditions. We apply again the classical linking theorem to ensure that such problem possesses a nontrivial weak solution. Finally, we prove that the quasilinear problem {(-∆u+V(x)u-u∆(u^2)=g(x,u) em R^3,@u∈H^1 (R^3)\\{0},)┤ where the potential V changes sign and may be unbounded from below and the nonlinearity g(x,u), as|x|→∞, has a kind of monotonicity, has a nontrivial weak solution. The existence of such solution is proved by means of a change of variables that makes the problem become a semilinear problem and hence allow us apply the mountain pass theorem combined with splitting lemma.
Liu, Yu-Yu. "Ground and Bound States of Nonlinear Schr dinger Equation." 2007. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-1907200703060200.
Full textHo, Sue Ching, and 何淑琴. "Estimates on the Eigenvalues for Schr$\ddot{rm o}$dinger Equation." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/79102607136289586062.
Full textYa-LinHuang and 黃雅琳. "Stability of Solitary Waves for the Zakharov Equations and the Fourth Order Nonlinear Schr"{o}dinger Equation." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/rf98bv.
Full text"Global Behavior Of Finite Energy Solutions To The Focusing Nonlinear Schrödinger Equation In d Dimension." Doctoral diss., 2011. http://hdl.handle.net/2286/R.I.9026.
Full textDissertation/Thesis
Ph.D. Mathematics 2011
Hsu, Bo-Wen. "Blow-up Solutions of Two-Coupled Nonlinear Schr dinger Equations." 2006. http://www.cetd.com.tw/ec/thesisdetail.aspx?etdun=U0001-2007200620091700.
Full textWu, Ren-Jie, and 吳仁傑. "Calculation of the time-dependent Schro ̈dinger equation in momentum space and the study of atomic multiphoton ionization." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/13373770632358451015.
Full text國立交通大學
物理研究所
99
Quantum mechanical wave function in momentum space with generalized pseudospectral method, we can save the amount of computation and that the error are small, and the result can be obtained with more easily way. Then we can apply those complete set of wave functions to other theory, such as perturbation theory, strong field approximation (SFA), etc., providing a simple and fast calculation tool to determine the motion of photonelectron in a strong laser field.