Abstract
When the Hamiltonian for a system is independent of time, there is an essential simplification in that the general solution of the Schrödinger equation can be expressed as a function of spatial coordinates and a function of time. Thus, assuming the potential energy function to be independent of time, the one-dimensional time dependent Schrödinger equation [see Eq. (25) of Chapter 4] is given by
where μ represents the mass of the particle. The above equation can be solved by using the method of separation of variables
Substituting in Eq. (1) and dividing by ψ(x, t), we obtain
Only questions about the results of experiments have a real significance and it is only such questions that theoretical physics has to consider.
P.A.M. Dirac in The Principles of Quantum Mechunics
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References
D. Halliday and R. Resnick, Physics Parts I & II, John Wiley, New York (1978).
S. Chandrasekhar, Introduction to the Study of Stellar Structure, Dover Publications, New York (1957).
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© 2004 Springer Science+Business Media Dordrecht
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Ghatak, A., Lokanathan, S. (2004). Bound State Solutions of the Schrödinger Equation. In: Quantum Mechanics: Theory and Applications. Fundamental Theories of Physics, vol 137. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2130-5_6
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DOI: https://doi.org/10.1007/978-1-4020-2130-5_6
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