it appears you have not given a proper listing for g(x,t), as you just have the definiton of repeated there.
it is also unclear how "x" is supposed to operate on a function g(x,t).
Just starting third level Uni. stuff & am faced with linear operators from Quantum Mechanics & need a little help.
OK, an operator, Ô, is said to be linear if it satisfies the equation
Ô(α f1 + β f2) = α(Ô f1) + β(Ô f2)
Fine
but I have an equation I can't wrap my head around, maybe just rusty, a hint would be nice, though.
Ô1 = d/dx;
Ô2 =3 d/dx +3x^2;
Find the new functions obtained by acting with each of these operators on
(a) g(x, t) =3 d/dx +3x^2
(b) h(x, t)=α sin(kx − ωt).
Now
Ô1 g(x,t) = 6xt^3
But not sure about how to get
Ô2 g(x,t) =
how to get this middle bit, please . . . . .
Answer is 18xt^3 + 9x^4 t^3
Okay, that is "differentiate the function".
This says "differentiate the function, then add x^2 and multiply by 3.Ô2 =3 d/dx +3x^2;
This is not a function. With that "d/dx" in it, it is another operator. Further, there is no "t" in it. In fact, this is the same as your definition of Ô2. I suspect you have copied the wrong thing.Find the new functions obtained by acting with each of these operators on
(a) g(x, t) =3 d/dx +3x^2
Take your previous answer, which was apparently 6xt^3, add x^2, and multiply by 3: 3(6xt^3+ x^2)= 18xt^3+ 3x^2.(b) h(x, t)=α sin(kx − ωt).
Now
Ô1 g(x,t) = 6xt^3[/quote\
This would be correct if g(x,t) were just 3x^2t^3 or that plus a constant.
But not sure about how to get
Ô2 g(x,t) =
I think you need to go back, read the problem again and see if you have not copied the first function incorrectly.how to get this middle bit, please . . . . .
Answer is 18xt^3 + 9x^4 t^3