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Suppose \(\langle p \mid \psi \rangle = e^{-\frac{ipx}{\hbar}}\). What is \(\langle x \mid \psi \rangle = ?\)

Options:
1. \( \sqrt{2\pi \hbar} \, \delta(x - x') \)
2. \( 2\pi \hbar \)
3. \( \frac{1}{\sqrt{2\pi \hbar}} \, \delta(x - x') \)
4. \( \delta(x - x') \)

Each option proposes a possible expression for the wave function \(\langle x \mid \psi \rangle\) given the initial condition. Here, \(\delta(x - x')\) represents the Dirac delta function, which is used to describe a discrete point in space.
Transcribed Image Text:Suppose \(\langle p \mid \psi \rangle = e^{-\frac{ipx}{\hbar}}\). What is \(\langle x \mid \psi \rangle = ?\) Options: 1. \( \sqrt{2\pi \hbar} \, \delta(x - x') \) 2. \( 2\pi \hbar \) 3. \( \frac{1}{\sqrt{2\pi \hbar}} \, \delta(x - x') \) 4. \( \delta(x - x') \) Each option proposes a possible expression for the wave function \(\langle x \mid \psi \rangle\) given the initial condition. Here, \(\delta(x - x')\) represents the Dirac delta function, which is used to describe a discrete point in space.
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