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Unformatted text preview: mate is above the true energy. Now do the reverse: Consider the attractive delta function potential V ( x ) =- ( x ). Use the ground state wavefunction of the harmonic oscillator as a variational trial wavefunction. Let the width vary. 4. Consider the attractive square well potential: V ( x ) =-, | x | < L : V ( x ) = 0 , | x | > L . Use a variational argument to show this potential has a bound state for any > 0 no matter how small. Argue that an extension of this argument shows that any attractive potential in one dimension has a bound state....
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- Spring '09