Question

2. The ground state (apart from normalization) of a particle of unit mass moving in a one-dimensional potential $V(x)$ is $\exp(-x^2/2)\cosh(\sqrt{2}x)$. The potential $V(x)$, in suitable units so that $\hbar=1$, is (up to an additive constant). (a) $\pi^2/2$ (b) $\frac{\pi^2}{2} - \sqrt{2}x \tanh(\sqrt{2}x)$ (c) $\frac{\pi^2}{2} - \sqrt{2}x \tan(\sqrt{2}x)$ (d) $\frac{\pi^2}{2} - \sqrt{2}x \coth(\sqrt{2}x)$

Name: 2 the ground state apart from normalization of a particle of unit mass moving in a one dimensional potential vx is exp x22coshsqrt2x the potential vx in suitable units so that hbar1 is up to 92677
Uploaded: 2023-07-18T05:59:02-08:00
Duration: 3 min 53 s
Channel: Madhur L
Description: 2 the ground state apart from normalization of a particle of unit mass moving in a one dimensional potential vx is exp x22coshsqrt2x the potential vx in suitable units so that hbar1 is up to 92677

          2. The ground state (apart from normalization) of a particle of unit mass moving in a one-dimensional potential $V(x)$ is $\exp(-x^2/2)\cosh(\sqrt{2}x)$. The potential $V(x)$, in suitable units so that $\hbar=1$, is (up to an additive constant).
(a) $\pi^2/2$
(b) $\frac{\pi^2}{2} - \sqrt{2}x \tanh(\sqrt{2}x)$
(c) $\frac{\pi^2}{2} - \sqrt{2}x \tan(\sqrt{2}x)$
(d) $\frac{\pi^2}{2} - \sqrt{2}x \coth(\sqrt{2}x)$

2 the ground state apart from normalization of a particle of unit mass moving in a one dimensional potential vx is exp x22coshsqrt2x the potential vx in suitable units so that hbar1 is up to 92677

Added by Ashley G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/18/2023

Step 1

The ground state wavefunction is given by $$\psi(x) = \exp(-x^2/2)\cosh(\sqrt{2}x)$$ We need to find the potential $V(x)$. Show more…

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2. The ground state (apart from normalization) of a particle of unit mass moving in a one-dimensional potential $V(x)$ is $\exp(-x^2/2)\cosh(\sqrt{2}x)$. The potential $V(x)$, in suitable units so that $\hbar=1$, is (up to an additive constant). (a) $\pi^2/2$ (b) $\frac{\pi^2}{2} - \sqrt{2}x \tanh(\sqrt{2}x)$ (c) $\frac{\pi^2}{2} - \sqrt{2}x \tan(\sqrt{2}x)$ (d) $\frac{\pi^2}{2} - \sqrt{2}x \coth(\sqrt{2}x)$