Question

#4. A particle in the simple harmonic potential starts out in the state: $\Psi(x,0) = \frac{1}{\sqrt{2}} \left[ \psi_0(x) + \psi_1(x) \right]$ where $\psi_0(x)$ & $\psi_1(x)$ are the ground state & first excited state of the time independent equation. (a) Construct $\Psi(x,t)$ (b) Find $<x>$ as a function of time, using lowering praising operators. plot it. (c) Find $<H>$ as a function of time. How does the time dependence of the operator in b) and this one differ?

          #4. A particle in the simple harmonic potential starts out in the state:
$\Psi(x,0) = \frac{1}{\sqrt{2}} \left[ \psi_0(x) + \psi_1(x) \right]$
where $\psi_0(x)$ & $\psi_1(x)$ are the ground state & first excited state
of the time independent equation.
(a) Construct $\Psi(x,t)$
(b) Find $<x>$ as a function of time, using lowering praising operators.
plot it.
(c) Find $<H>$ as a function of time. How does the time dependence of the
operator in b) and this one differ?

#4. A particle in the simple harmonic potential starts out in the state:
Ψ(x,0) = (1)/(√(2))[ ψ0(x) + ψ1(x) ]
where ψ0(x) ψ1(x) are the ground state first excited state
of the time independent equation.
(a) Construct Ψ(x,t)
(b) Find <x> as a function of time, using lowering praising operators.
plot it.
(c) Find <H> as a function of time. How does the time dependence of the
operator in b) and this one differ?

Added by Antonio G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Hunza Gilgit

01/14/2022

Step 1

In order to solve the system of equations, we need to identify the constants and variables. The constants are C3 and 0, and the variables are the harmonic potential (H) and the time (t). #2. To solve the system of equations, we need to use the lowering Show more…

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A particle in the Simple Harmonic Potential starts out in the state: (x0, p0) = (c3,0) - (c4,0) + (4,0) of the time-independent equation (a Constant). Find <x as a function of time using lowering and raising operators and plot it. Find <H as a function of time. How does the time dependence of the operator in b) and this one differ?