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kl14
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Homework Statement
particle in ground state of 1D harmonic oscillator - spring constant is doubled - what is the probability of finding the particle in the ground state of the new potential
Homework Equations
v=1/2kx^2 oscillator potential
wavefunction ground state n=0 = (alpha/pi)^1/4*e^[(-apha*x^2)/2]
alpha = sqroot[(k*m)/hbar^2)]
The Attempt at a Solution
the probability will be = integral[wavefunction old*wavefunction new]dx
initial equation d^2psi/dx^2 + [2m(E-1/2kx^2)/hbar]psi = 0
if you double k in the potential V(x)- the equation is d^2psi/dx^2 + [2m(E-kx^2)/hbar]psi = 0
does this change alpha to 2k? this makes the integral very complex to solve.
or can this be done by changing the wavefunction for the new potential to (alpha/2pi)^1/4*e^[(-apha*x^2)/2]
the change being 2pi - doubling the range of the spring constant?
Thanks!