Using a variational method to obtain the ground state of the quantum Hamiltonian: symbolic computation approach. (English) Zbl 1421.81043


81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
35A15 Variational methods applied to PDEs
68W30 Symbolic computation and algebraic computation
97M50 Physics, astronomy, technology, engineering (aspects of mathematics education)


SAGE Interacts
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[1] Cooper, F.; Khare, A.; Sukhatme, U., Supersymmetry and quantum mechanics, Phys. Rep., 251, 267, (1995)
[2] Laughlin, R. B., Anomalous quantum hall effect: an incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett., 50, 1395, (1983)
[3] Chhabra, M.; Das, R., Quantum mechanical wavefunction: visualization at undergraduate level, Eur. J. Phys., 38, (2016)
[4] Stein, W., (2008)
[5] Finch, C., SAGE Beginner’s Guide, (2011), Birmingham: Packt Publishing, Birmingham
[6] Mezei, R. A., An introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods, (2016), Hoboken, NJ: Wiley, Hoboken, NJ · Zbl 1342.65249
[7] Ghatak, A.; Lokanathan, S., Quantum Mechanics: Theory and Applications, (2005), New Delhi: MacMillan India, New Delhi · Zbl 1059.81001
[8] Fernandez, F. M.; Ma, Q.; Tipping, R. H., Tight upper and lower bounds for energy eigenvalues of the Schrodinger equation, Phys. Rev. A, 39, 1605, (1989)
[9] Vallée, O.; Soares, M., Airy Functions and Applications to Physics, (2004), London: Imperial College Press, London · Zbl 1056.33006
[10] Reed, B. C., Variational Treatment of the linear potential, Am. J. Phys., 58, 407, (1990)
[11] Mohallem, J. R., Comment on ‘Variational treatment of the linear potential,’ by B Cameron Reed (1990 Am. J. Phys. 58 407), Am. J. Phys., 59, 852, (1991)
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