Exact solution for 1D Schrodinger equation needed!

[johnnybravo]

Not sure if this is the right place to ask, or if anyone will respond -- I just need somebody's help desperately: Meron bang exact solution ang Morse potential TISE? May nakita akong website na kinukumpara qualitatively yung eigenstate separations ng harmonic oscillator tsaka Morse potential... though no formal solution was presented. Thanks in advance.

[jana_atenista]

sure si me mga fellow ateneans ko pow makaksagot nyan... were great po in Math and Science.. not only in Law. Ateneans post na po tayo! lets help him na...

GO GO GO! Ateneo!

[flsfnoeraekadad]

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html

1d Schrodinger

http://www.chem.csus.edu/poster/morse/morse.htm

Morse Potential

[flsfnoeraekadad]

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html

1d Schrodinger

http://www.chem.csus.edu/poster/morse/morse.htm

Morse Potential

I'm sorry I can't furthermore go. Physics is not my forte. :( I hope I helped kahit konting-konting-konti.

[paparagon]

ang tindi ng schrodinger equation na un- may wave function, step function at partial derivative. lol kailangan astigin *** math mo.

*** isa exponential*something. bigay mo *** differential equation baka masagutan natin.

wala kanabang ibang description para sa problem?

[johnnybravo]

hey! didn't expect people to respond to this! Salamat sa mga reply. Anyway for the 1D case, ok yung nasa http://www.chem.csus.edu/poster/morse/morse.htm, pero para sana mas maayos yung problema, mas maganda kung magpuntang zero yung function sa asymptote na x--> +infinity, i.e.

U(x) = D[(exp(-a(x-x0))-1)^2-1]

where D--> depth ng well
x0 --> position ng minimum
a --> range parameter

Alam ko dapat may nakasolve na nito e, pero kung libre kayo, kailangan ko lang mahanap yung solution nung Time Independent Schodinger Equation sa http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/scheq.html, gamit yung U(x) sa taas.

Hahagilap pa ako ng mga libro.

SALAMAT NANG MARAMI!

[paparagon]

masyadong messed-up *** math- di ko kaya mag-solve ng multivariable differential equation. brutal *** math na yan ha! gumamit ka nalang ng software para masagutan (suggest ko maple).