Possible analytical solution of transcendental equation by an assumption.

  • Thread starter Azorspace
  • Start date
Is it possible to solve the next transcendental equation analytically (obviously for k):


making the assumption that (bl >>1). I think that is not possible, but in an article that i found,
they solve it by making that assumption, and they reach to the solution:



E=-2cosh(k), Eo=-{(4+b²)^(1/2)}, and d=(2b²/|Eo|)(e^(-bl))

physically this problem corresponds to that of finding the energy of bound states in an infinite one dimensional regular lattice, with two embedded impurities.

Thanks everybody in advance.
Well... the solution they get isnt exact. But its precision is as great as the "goodness" of their assumption. In other words, as they assumed that bl>>1, as greater bl were, as precise their solution will be.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads