Old Guy
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Homework Statement
Homework Equations
(\langle \alpha | + \lambda^\ast\langle \beta |)(|\alpha\rangle+ \lambda|\beta\rangle) = \langle \alpha |\alpha \rangle + |\lambda|^2\langle \beta | \beta \rangle + \lambda \langle \alpha | \beta \rangle + \lambda^\ast \langle \beta | \alpha \rangle \geq 0<br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> This equation is the setup, and it leads to an equation that I can see is quadratic in lambda. From this, I calculate the discriminant, which must be greater than or equal to zero because all the terms are real and positive. However, when I manipulate this to get to the Schwarz inequality, I get a &quot;less than or equal to&quot; where I should have a &quot;greater than or equal to&quot;. Can somone please help? Thanks.<br />