12 citations · 57 across the 11 of their papers we have counts for
11 papers
Solvable model of bound states in the continuum (BIC) in one dimension
Zafar Ahmed, Sachin Kumar, Dona Ghosh +1
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 s…
Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials
Zafar Ahmed, Sachin Kumar, Dona Ghosh
For complex PT-symmetric scattering potentials (CPTSSPs) , we show that c…
Divergence of in discontinuous potential wells
Zafar Ahmed, Sachin Kumar, Dona Ghosh +1
The surprising divergence of the expectation value for the square well potential is known. Here, we prove and demonstrate the divergence of in potential wel…
Expectation values of and in the square well potential
Zafar Ahmed, Dona Ghosh, Sachin Kumar +1
Position and momentum representations of a wavefunction and , respectively are physically equivalent yet mathematically in a given case one may be easier or more trans…
Coherent scattering from semi-infinite non-Hermitian potentials
Zafar Ahmed, Dona Ghosh, Sachin Kumar
When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection and transmission …
Solvable models of an open well and a bottomless barrier in 1-D
Zafar Ahmed, Dona Ghosh, Sachin Kumar +1
We present one dimensional potentials as solvable models of a well and a barrier (). Apart from being new addition to solvable models, th…
Real discrete spectrum of complex PT-symmetric scattering potentials
Zafar Ahmed, Joseph Amal Nathan, Dhruv Sharma +1
We investigate the parametric evolution of the real discrete spectrum of several complex PT symmetric scattering potentials of the type $V(x)=-V_1 F_e(x) + i V_2 F_o(x), V_1>0, F_e…
Accidental crossings of eigenvalues in one-dimensional complex PT-symmetric Scarf-II potential
Zafar Ahmed, Dona Ghosh, Joseph Amal Nathan +1
So far, the well known two branches of real discrete spectrum of complex PT-symmetric Scarf II potential are kept isolated. Here, we suggest that these two need to be brought toget…
A new solvable complex PT-symmetric potential
Zafar Ahmed, Dona Ghosh, Joseph Amal Nathan
We propose a new solvable one-dimensional complex PT-symmetric potential as $V(x)= ig~ \mbox{sgn}(x)~ |1-\exp(2|x|/a)|$ and study the spectrum of . For smaller va…
A solution to Ahmed's Integral(II)
Dona Ghosh
In the year 2000, Ahmed proposed a family of integrals in the American Mathematical Monthly which invoked a considerable response then. Here I would like to present another solutio…
Transparency of the PT-symmetric complex potentials for coherent injection
Zafar Ahmed, Joseph Amal Nathan, Dona Ghosh
Two port s-matrix for a complex PT-symmetric potential may have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We…