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The ground state of a quantum/classical mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. When a quantum system has infinite possible ground states, it is gapless with massless modes; if a quantum system has finite ground states, it is known as gapped and potentially topologically ordered. The ground state of a quantum field theory is usually called the vacuum state or the vacuum.

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Estimate bound state energy for shallow finite well

It is well-known that the finite square well always has a bound state, no matter how shallow it is. Suppose the finite square well is given by $V(x) = -V_0$ for $-a\le x \le a$. The standard result is …