you leave x as an unknown. Instead you will need equate the coefficients of x^{0},x^{1},x^{2}
this will give you enough equations to solve for A,B and C
You need to make the three "fractions" you have on the LHS into just one "fraction" (google "addition and subtraction of algebraic fractions" as a hint).
once you have that you can then equate the denominators numerators in a separate equation. Then you can start to solve for A, B and C
thanks so much! this has been bothering me all day!
I used \left[ a,a^{t}\right]= a a^{t}-a^{t} a =1
and re-arranged to get
a a^{t}-1=a^{t} a
which I then sub straight into the first line :-)
Apologies I mistyped when I wrote
Ha^{t}\left|\Psi\right\rangle
I meant to say Ha\left|\Psi\right\rangle
does this make more sense now?
It now looks just like your second hamiltonian multiplied by "a" to me.
Homework Statement
Hi, I'm currently studying for a quantum mechanics exam but I am stuck on a line in my notes:
Ha\left|\Psi\right\rangle =\hbar\omega\left(a^{t}a a + \frac{a}{2}\right)\left|\Psi\right\rangleHa\left|\Psi\right\rangle =\hbar\omega\left(\left(a a^{t} - 1\right)a +...
Homework Statement
Hi, I am trying to show that ( \lambda \hat{1})^{t} = \lambda^* \hat{1}
where \lambda \in C (complex numbers)
and \hat{1} is the identity operator.
The Attempt at a Solution
\int \Psi^* (\lambda \hat{1} )^{t} \Psi d^{3} {r} = \int (\lambda \hat{1}...