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Full-Text Articles in Physical Sciences and Mathematics
Schrödinger, 2, David Peak
Schrödinger, 2, David Peak
Schrodinger
The finite square well
The infinite square well potential energy rigorously restricts the associated wavefunction to an exact region of space: it is infinitely “hard.” Potential energies encountered in more realistic physical scenarios are “softer” in that they permit wavefunctions to spread throughout less well-defined regions. An important toy example of the latter is the finite square well. In this problem, the potential energy function is U(x) = 0, if 0 < x < L, and U0 otherwise.
Schrödinger, 3, David Peak
Schrödinger, 3, David Peak
Schrodinger
The 3D infinite square well: quantum dots, wells, and wires
In the preceding discussion of the Schrödinger Equation the particle of interest was assumed to be “moving in the x -direction.” Of course, it is not possible for a particle to be moving in one spatial direction only. If that were true, according to the HUP it could be anywhere in the y - and z -directions and therefore be undetectable with finite volume detectors. Now, we consider the more realistic case of motion in all three spatial directions. For this purpose, we start with the 3D infinite square well. …
Schrödinger, 5, David Peak
Schrödinger, 4, David Peak
Schrödinger, 4, David Peak
Schrodinger
The sanitized hydrogen atom: separating the variables
Separation of variables in the Schrödinger Equation for the hydrogen problem requires expressing Ψ as a product, Ψ(r,θ,φ,t) = R(r)Θ(θ )Φ(φ)T(t) , substituting into the partial differential equation [(5) in Sc3], and then dividing by Ψ. As in the square well problems, the separation constant for the t part of the separation is the particle’s eigen-energy, E.