Question

Consider a particle of mass $m$ in an infinite one dimensional square well of width $2a$: $V(x) = 0$ for $|x| < a$ $= \infty$ for $|x| > a$ (1) with $a$ a positive constant. a) Estimate the ground state energy by using the variational wavefunction $\psi(x) = A(a^\lambda - |x|^\lambda)$ $|x| < a$, 0 otherwise (2) where $\lambda > 0$ is the variational parameter and A an appropriate normalization constant (which you need to evaluate!). What is the % error of this estimate compared to the (known) exact ground state energy? Note: You should use the fact that this is a symmetric wavefunction, as well as an ex- pression for the kinetic energy that we derived in the lectures that avoids second derivatives.

          Consider a particle of mass $m$ in an infinite one dimensional square well of width $2a$:
$V(x) = 0$ for $|x| < a$
$= \infty$ for $|x| > a$
(1)
with $a$ a positive constant.
a) Estimate the ground state energy by using the variational wavefunction
$\psi(x) = A(a^\lambda - |x|^\lambda)$ $|x| < a$, 0 otherwise
(2)
where $\lambda > 0$ is the variational parameter and A an appropriate normalization constant (which
you need to evaluate!). What is the % error of this estimate compared to the (known) exact
ground state energy?
Note: You should use the fact that this is a symmetric wavefunction, as well as an ex-
pression for the kinetic energy that we derived in the lectures that avoids second derivatives.

Consider a particle of mass m in an infinite one dimensional square well of width 2a:
V(x) = 0 for |x| < a
= ∞ for |x| > a
(1)
with a a positive constant.
a) Estimate the ground state energy by using the variational wavefunction
ψ(x) = A(a^λ - |x|^λ) |x| < a, 0 otherwise
(2)
where λ > 0 is the variational parameter and A an appropriate normalization constant (which
you need to evaluate!). What is the % error of this estimate compared to the (known) exact
ground state energy?
Note: You should use the fact that this is a symmetric wavefunction, as well as an ex-
pression for the kinetic energy that we derived in the lectures that avoids second derivatives.

Added by Martin P.

Question

Please give Ace some feedback