(adsbygoogle = window.adsbygoogle || []).push({}); bounded solutions of a system of coupled liniar Schrodinger equations

Hi.

I study the following system of four coupled liniar Schrodinger equations:

[itex]

i\delta \left(\begin{array}{c}f&h&g&q \end{array}\right) =

\left(\begin{array}{cccc}

-L_p&-a_1&-a_2&-a_2\\

a_1&L_p&a_2&a_2\\

-a_3&-a_3&-L_c&-a_4\\

a_3&a_3&a_4&L_c

\end{array}\right)

\left(\begin{array}{c}f&h&g&q \end{array}\right)

[/itex]

where [itex]L_{p,c}=\frac{d^2}{dr^2}+\frac{1}{r}\frac{d}{dr}-\frac{m^2}{r^2}-\beta_{p,c}[/itex]

[itex]\beta_{p,c}>0[/itex], [itex]m[/itex] is integer.

The coeficients [itex]a_j(r)[/itex] are real functions given numerically, they have no singularity on [itex][0,\infty)][/itex], and they fulfill

[itex]\lim_{r\rightarrow\infty} a_j(r)=0[/itex]

I am interested in finding the bound states [itex](f,h,g,q)[/itex] and their eigenvalues, or at least finding some condition for their existence. I will appreciate any idea or any reference (book or article) on how one might solve this problem. I must say that I am physicist.

Thank you.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Bounded solutions of a system of copled liniar Schrodinger equations

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**