- #1
neelakash
- 511
- 1
Homework Statement
Consider the following problem:
if [tex]\ A [/tex][tex]\psi=[/tex][tex]\lambda[/tex][tex]\psi[/tex],prove that
[tex]\ e ^ A [/tex][tex]\psi=[/tex][tex]\ e ^\lambda[/tex][tex]\psi[/tex]
Homework Equations
The Attempt at a Solution
This is my attempt.Please check if I am correct.
If
[tex]\ e ^ A [/tex][tex]\psi=[/tex][tex]\ e ^\lambda[/tex][tex]\psi[/tex]
is correct, we should have:
[tex]\ ln [/tex][tex]\ e^ A [/tex][tex]\psi=[/tex][tex]\ ln [/tex][tex]\ e ^\lambda[/tex][tex]\psi[/tex]
or, [tex]\ ln \{e^A} + [/tex][tex]\ ln \psi=[/tex][tex]\ ln \{e^\lambda} + [/tex][tex]\ ln \psi[/tex]
Now cancel [tex]\ ln \psi[/tex] from both sides and post-multiply the resulting equation by [tex]\psi[/tex]
That is---
[tex]\ ln \{e^A} =[/tex][tex]\ ln \{e^\lambda}[/tex]
or, [tex]\ [ln \{e ^ A}][/tex][tex]\psi=[/tex][tex]\ [ln \{e ^\lambda}][/tex][tex]\psi[/tex]
Alternatively,
[tex]\ A [/tex][tex]\psi=[/tex][tex]\lambda[/tex][tex]\psi[/tex]
So, we got the given equation from the equation to be proved.
Last edited: