well that's kind of what I'm asking... is there a way to arrive at that determinant form without knowing a x b equals |a||b|sin(theta)? So we want to construct a vector that is perpendicular to 2 vectors in a plane and has a magnitude that somehow expresses the amount of rotation.
the dot product allows you to multiply a vector A with the component of another vector B that lies along A. For instance in order to find the quantity work which is force times distance, we multiply the component of force applied in the direction of the displacement with the displacement. We...
I guess another way of what I am asking is - is there any way to arrive at the component form of the cross product without knowing it is equal to absin(theta)?
I'm having trouble relating the cross product form |a||b|sin(theta) to its component form (a1b2 - a2b1) ... and so on... I know how to do this mathematically so please don't just suggest some proof that I can find in every textbook... The component form involves the solutions to equations...
Homework Statement
a = x + \frac{d}{dx}
Construct the Hermitian conjugate of a. Is a Hermitian?
2. The attempt at a solution
<\phi|(x+\frac{d}{dx})\Psi>
\int\phi^{*}(x\Psi)dx + <-\frac{d}{dx}\phi|\Psi>
I figured out the second term already but need help with first term... am...
I need to solve the equation
\frac{d^{2}}{dx^{2}}\Psi + \frac{2}{x}\frac{d}{dx}\Psi = \lambda\Psi
Can anyone help me get a start on this problem? I've been guessing at a few solutions with no results... I'm not asking anyone to solve the problem... just a few hints on starting... maybe...
I need to solve the equation
\frac{d^{2}}{dx^{2}}\Psi + \frac{2}{x}\frac{d}{dx}\Psi = \lambda\Psi
Can anyone help me get a start on this problem? I've been guessing at a few solutions with no results... I'm not asking anyone to solve the problem... just a few hints on starting... maybe...
Homework Statement
Find the eigenfunctions and eigenvalues for the operator:
a = x + \frac{d}{dx}
2. The attempt at a solution
a = x + \frac{d}{dx}
a\Psi = \lambda\Psi
x\Psi + \frac{d\Psi}{dx} = \lambda\Psi
x + \frac{1}{\Psi} \frac{d\Psi}{dx} = \lambda
x + \frac{d}{dx}...