- #1

musicmar

- 100

- 0

## Homework Statement

Combine Eqs. 4.4 and 4.5 to derive Eq. 4.22

## Homework Equations

4.4: p= m u/ (sqrt(1-(u

^{2}/c

^{2})))

4.5: E= m c

^{2}/ (sqrt(1-(u

^{2}/c

^{2})))

4.22: E

^{2}-(pc)

^{2}= (mc

^{2})

^{2}

## The Attempt at a Solution

(sqrt(1-(u

^{2}/c

^{2}))) = mu/p

(sqrt(1-(u

^{2}/c

^{2}))) = mc

^{2}/E

1 - u

^{2}/c

^{2}= m

^{2}u

^{2}/p

^{2}

1 - u

^{2}/c

^{2}= m

^{2}c

^{4}/E

^{2}

u

^{2}/c

^{2}=1-m

^{2}u

^{2}/p

^{2}

u

^{2}/c

^{2}=1-m

^{2}c

^{4}/E

^{2}

Now combining:

1 - m

^{2}u

^{2}/p

^{2}=

1 -m

^{2}c

^{4}/E

^{2}

m

^{2}u

^{2}E

^{2}=m

^{2}c

^{4}p

^{4}

Clearly, this is not Eq. 4.22 above. So, I either made a small mistake somewhere or missed a larger concept.

Thank you.