Purchase Solution

# Hydrogen atom ground state, uncertainty relation

Not what you're looking for?

Hydrogen atom ground state, uncertainty relation

See full description in the attached file.

##### Solution Summary

The solution discusses the hydrogen atom ground state, and uncertainty relation.

##### Solution Preview

See the attached file.

Here is a plain TEX source for search:

From the table, we find that the normalized 1s wave function for Z=1 is
\$\$
psi(vec r) = psi_{000} = {1oversqrt{pi a_o^3}} e^{-r/a_o}.
eqno(1.1)
\$\$

bf (a) rm

Since \$psi(vec r)\$ is symmetric about the origin, we have \$la xra = 0\$ and also
\$\$
la x^2ra = la y^2ra = la z^2ra = {1over 3} la x^2 +y^2+z^2ra
= {1over 3} la r^2ra = {1over 3}int d^3vec r r^2|psi|^2 =
\$\$
\$\$
= {1over 3pi a_o^3} int_0^pi sintheta dtheta int_0^{2pi} dphi
int_0^infty r^2dr r^2e^{-2r/a_o}
= {4piover 3pi a_o^3}int_0^infty r^4e^{-2r/a_o} dr,
eqno(1.2)
\$\$
where \$(r,theta,phi)\$ are spherical coordinates. ...

##### Classical Mechanics

This quiz is designed to test and improve your knowledge on Classical Mechanics.

##### The Moon

Test your knowledge of moon phases and movement.

##### Intro to the Physics Waves

Some short-answer questions involving the basic vocabulary of string, sound, and water waves.

##### Variables in Science Experiments

How well do you understand variables? Test your knowledge of independent (manipulated), dependent (responding), and controlled variables with this 10 question quiz.

##### Introduction to Nanotechnology/Nanomaterials

This quiz is for any area of science. Test yourself to see what knowledge of nanotechnology you have. This content will also make you familiar with basic concepts of nanotechnology.