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The lowest values of ζ = |ζ| (E ζ > 0) as a function of the coupling constant g. Dashed lines for |ζ| = 2n (n = 1, 2, 3, . . .), corresponding to odd-parity eigenfunctions. Continuous lines for numerical solutions of the transcendental equation 1 g |ζ|π 2 = tan |ζ|π 2

The lowest values of ζ = |ζ| (E ζ > 0) as a function of the coupling constant g. Dashed lines for |ζ| = 2n (n = 1, 2, 3, . . .), corresponding to odd-parity eigenfunctions. Continuous lines for numerical solutions of the transcendental equation 1 g |ζ|π 2 = tan |ζ|π 2

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Figure 1: The lowest values of ζ = |ζ| (E ζ > 0) as a function of the...
Figure 2: The probability densities ρ (e) ζ (x) = |ψ (e) ζ (x) | 2 for...
Revisiting the bound states of a confined delta potential
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  • Feb 2024
The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the litera...
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... doublet structure in the spectrum serves as a clear indication of the double degeneracy associated with the limit |g| → ∞. To enhance precision and clarity, the exact numerical solution of equation (51) for the six lowest values of |ζ| is presented in Fig.1. ...

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