Ansatz: Principle, Hypothesis, Boundary Condition?

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An ansatz is a proposed solution used in various fields, including physics, to simplify complex problems, such as in the Bethe ansatz for quantum systems. It serves as a hypothesis or assumption that guides the solution process, often involving boundary conditions or self-consistency conditions. The Heisenberg system adheres to the ansatz, which raises questions about its potential violations and the criteria for verifying its accuracy. While it cannot always be deduced, its validity is often supported by empirical evidence and theoretical consistency. Ultimately, the ansatz is crucial for deriving exact solutions in complex systems.
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What is ansatz? such as Bethe ansatz. Is it a principle? hypothesis? or boundary condition? self-consistency condition? Why the Heisenberg system has to obey the ansatz? Could it be violated? If it can not be deduced, how could we verify it is true? and why do we believe the solution is exact?
 
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An ansatz is in general a proposal for a solution.

For example when you are solvning PDE's, and have homogenous BC, you often make the ansatz of separation variables. etc.

http://en.wikipedia.org/wiki/Ansatz
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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