arXiv subjects

Tarit Goswami

Publications and source records attributed to Tarit Goswami.

2 recordsLinked to original sources

arXiv2019

Symmetric Fermi-type potential

We utilize the amenability of the Fermi-type potential profile in Schr{ö}dinger equation to construct a symmetric one dimensional well as $V(x){=}{-}U_n/[1+\exp[(|x|{-}a)/b]], ~ U_n{=}V_n[1+\exp[-a/b]]$. We define $α=a/b, ~β_n {=}b\sqrt{2m U_n}/\hbar$, we find $β_n$ values for which critically the well has $n$-node half bound state at $E{=}0$. Consequently, this fixed well has $n$ number of bound states. Also we obtain a semi-classical expression ${\cal G}(α,β)$ such that the Fermi well has either $[\cal G]$ or $[{\cal G}]+1$ number of bound states. Here $[.]$ indicates the integer part. We also confirm the consistency of $\cal G$ with the number of s-wave neutron energy levels in a central ($x\in (0,\infty))$ Fermi potential well.

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arXiv2019

Solvable model of bound states in the continuum (BIC) in one dimension

Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory, central potentials. One dimensional version of BIC has long been attempted, where only quasi-exactly-solvable models have succeeded but not without instigating degeneracy in one dimension. Here, we present an exactly solvable bottomless exponential potential barrier $V(x)=-V_0[\exp(2|x|/a)-1]$ which for $E V_0$, there is again a continuum of complex scattering solutions $ψ(x)$ whose real and imaginary parts though solutions of Schr{ö}dinger equation yet their parities cannot be ascertained as $Cψ(x)$ is also a solution where $C$ is an arbitrary complex non-real number.

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