Question

2. A particle of mass $m$ is in the state $Psi(x,t) = Ae^{-a[(mx^2/2hbar)+it]}$ in the region $-infty$ to $+infty$ where $A$ and $a$ are constants. (a) Find the normalization constant $A$. (b) Calculate the expectation values of $p$ and $p^2$. (c) Calculate the uncertainty $Delta p$ using the results of (b) above.

          2. A particle of mass $m$ is in the state
$Psi(x,t) = Ae^{-a[(mx^2/2hbar)+it]}$ in the region $-infty$ to $+infty$
where $A$ and $a$ are constants.
(a) Find the normalization constant $A$.
(b) Calculate the expectation values of $p$ and $p^2$.
(c) Calculate the uncertainty $Delta p$ using the results of (b) above.

2. A particle of mass m is in the state
Psi(x,t) = Ae^-a[(mx^2/2hbar)+it] in the region -infty to +infty
where A and a are constants.
(a) Find the normalization constant A.
(b) Calculate the expectation values of p and p^2.
(c) Calculate the uncertainty Delta p using the results of (b) above.

Added by Christopher L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

03/20/2023

Step 1

The normalization condition is given by: $$\int_{-\infty}^{\infty} |\Psi(x,t)|^2 dx = 1$$ For the given wave function, we have: $$\Psi(x,t) = Ae^{a\left(\frac{mx^2}{2\hbar} + it\right)}$$ Now, let's find the square of the magnitude of the wave Show more…

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A particle of mass m is in the state Ψ(x,t) = Ae^{-a[(mx^2 /2ħ)+it]} in the region -∞ to +∞ where A and a are constants. (a) Find the normalization constant A. (b) Calculate the expectation values of p and p^2. (c) Calculate the uncertainty Δp using the results of (b) above.