Analytic solutions for <mml:math alttext="$q\bar q$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi><mml:mover accent="true"><mml:mi>q</mml:mi><mml:mo>&#xAF;</mml:mo></mml:mover></mml:math> systems obtained from a cut-off type approximation to the funnel potential are applied to <mml:math alttext="$b\bar b$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>b</mml:mi><mml:mover accent="true"><mml:mi>b</mml:mi><mml:mo>&#xAF;</mml:mo></mml:mover></mml:math> and <mml:math alttext="$c\bar c$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mi>c</mml:mi><mml:mo>&#xAF;</mml:mo></mml:mover></mml:math> systems. Perturbative corrections to oscillator energy levels due to inclusion of short range
<mml:math alttext="${a \mathord{\left/  {\vphantom {a r}} \right.  \kern-\nulldelimiterspace} r}$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>a</mml:mi><mml:mo>/</mml:mo><mml:mi>r</mml:mi></mml:mrow></mml:math> effect are also obtained.

Analytic approach to <mml:math alttext="$q\bar q$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi><mml:mover accent="true"><mml:mi>q</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> systems in potential models

Analytic approach to <svg style="vertical-align:-3.50804pt" height="16.362499" version="1.1" viewBox="0 0 16.8125 16.362499" width="16.8125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.925)"><path id="x1D45E" d="M474 429q-19 -69 -47 -222l-65 -347q-8 -49 0 -60t49 -16l26 -3l-4 -26l-246 -12l4 25l17 3q37 6 50 20.5t23 60.5l67 321h-2q-65 -79 -150 -138q-69 -47 -104 -47q-28 0 -48.5 32t-20.5 81q0 78 35 148t90 117q67 57 161 77q23 5 58 5q43 0 90 -15zM387 387&#xA;q-30 16 -75 16q-58 0 -92 -27q-49 -39 -78.5 -112t-29.5 -136q0 -34 8.5 -52.5t21.5 -18.5q40 0 109.5 63.5t103.5 115.5q16 53 32 151z" /></g><g transform="matrix(1.25,0,0,-1.25,90,90)"><path d="m -65.27,70.93 6.67,0" style="fill:none;stroke:#000000;stroke-width:0.68000001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none" /></g><g transform="matrix(.017,-0,0,-.017,8.413,11.925)"><use xlink:href="#x1D45E"/></g></svg> systems in potential models


International Journal of Mathematics and Mathematical Sciences

Analytic approach to qq¯ systems in potential models

Abstract

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