Question:
Given a system with non-positive energy and energy = 0 at infinity, do it have a bound state.
Solution:
For delta potential, we already know the answer, for 1 or 2 dimension we have bound state but for 3 we don't.
A reasonable conjecture, would then be, to conjecture we always have bound state for 1 or 2 dimension potential well, and may or may not have a bound state for 3 dimension.
It turns out to be true. See this as a theorem.
http://physics.stackexchange.com/questions/143630/why-the-statement-there-exist-at-least-one-bound-state-for-negative-potential
Given a system with non-positive energy and energy = 0 at infinity, do it have a bound state.
Solution:
For delta potential, we already know the answer, for 1 or 2 dimension we have bound state but for 3 we don't.
A reasonable conjecture, would then be, to conjecture we always have bound state for 1 or 2 dimension potential well, and may or may not have a bound state for 3 dimension.
It turns out to be true. See this as a theorem.
http://physics.stackexchange.com/questions/143630/why-the-statement-there-exist-at-least-one-bound-state-for-negative-potential
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