- #1
AxiomOfChoice
- 533
- 1
What is an "ansatz?"
I am reading a quantum mechanics textbook, and they keep talking about different kinds of ansatz's - most commonly, separation ansatz's. But I thought that an ansatz was nothing more than an educated guess! If you show that your ansatz is *a* solution to the Schrodinger equation, do you then know that it is *the* solution?
For example, in the two-body problem in quantum mechanics, how can you assume that [itex]\psi(\mathbf{x}_{cm}) = e^{i \mathbf{k}_{cm} \cdot \mathbf{x}_{cm}}[/itex] is the solution to [itex]H_{cm} \psi_{cm} = E_{cm} \psi_{cm}[/itex]?
I am reading a quantum mechanics textbook, and they keep talking about different kinds of ansatz's - most commonly, separation ansatz's. But I thought that an ansatz was nothing more than an educated guess! If you show that your ansatz is *a* solution to the Schrodinger equation, do you then know that it is *the* solution?
For example, in the two-body problem in quantum mechanics, how can you assume that [itex]\psi(\mathbf{x}_{cm}) = e^{i \mathbf{k}_{cm} \cdot \mathbf{x}_{cm}}[/itex] is the solution to [itex]H_{cm} \psi_{cm} = E_{cm} \psi_{cm}[/itex]?