Finding the Correct Equation for Heisenberg's Uncertainty Principle

[Lancelot59]

I'm given a form of Heisenberg's uncertainty principle in the form of:

$$\Delta E\Delta t\geq h$$

I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm.

Now given the relationship is on on a relative scale I used the approximation:
$$\Delta E\Delta t\approx h$$

I then used the following formula:

$$E=\frac{hc}{\lambda}$$
and differentiated like so:
$$\Delta E = -\frac{hc}{\lambda ^{2}}\Delta \lambda$$
Which I then substituted back in:

$$(-\frac{hc}{\lambda ^{2}}\Delta \lambda)\Delta t \approx h$$

Is this correct so far?

 

[dimension10]

I'm given a form of Heisenberg's uncertainty principle in the form of:

$$\Delta E\Delta t\geq h$$

I need to determine a time interval which would allow a laser to cover the whole visible spectrum, from 400 to 700nm.

Now given the relationship is on on a relative scale I used the approximation:
$$\Delta E\Delta t\approx h$$

I then used the following formula:

$$E=\frac{hc}{\lambda}$$
and differentiated like so:
$$\Delta E = -\frac{hc}{\lambda ^{2}}\Delta \lambda$$
Which I then substituted back in:

$$(-\frac{hc}{\lambda ^{2}}\Delta \lambda)\Delta t \approx h$$

Is this correct so far?

Actually, the equation is not correct (I'm assuming h to be the Planck's constant). It would be:

$$ \delta E\mbox{ }\delta t\geq\frac{\hbar}{2}=\frac{h}{4\pi} $$

Also, I don't see what you differentiated with respect to.

 

[Lancelot59]

Actually, the equation is not correct (I'm assuming h to be the Planck's constant). It would be:

$$ \delta E\mbox{ }\delta t\geq\frac{\hbar}{2}=\frac{h}{4\pi} $$

So if you were to use the correct equation with the same method, then you would have been correct.

I see the issue. The problem set gave us the wrong h...I'll re run it and let you know the result.

EDIT: I'm confused now. Should I be using h bar in all of the locations? This error in the problem set has mixed me up.