Recent content by Numnum

I'm not sure what you're asking. I multiplied by |e^{i\alpha t \hbar/m}| because to normalize a wave function I have to multiply by its complex conjugate and get e^0. For the final answer, did I forget to square the e^{-αx^2}? I just did right now and my final answer is A=...

|e^{-αx^2}||e^{-iαt\hbar/m}| Take the complex conjugate. |e^{-αx^2}||e^{-iαt\hbar/m}||e^{iαt\hbar/m}| And I'm left with this. e^{-αx^2} Then, 1= |A|^2\int^{\infty}_{-\infty}e^{-αx^2}dx 1= |A|^2√(\pi/α) A= a^{1/4}/\pi^{1/4} Did I get there?

Homework Statement A quantum mechanical wavefunction for a particle of mass m moving in one dimension where α and A are constants. Normalize the function - that is find a value of A for which \int^{\infty}_{-\infty}|ψ|^2dx=1 Homework Equations ψ(x,t)= |Ae^{-α(x^2 + it\hbar/m)}|^2...

Thank you! But, that's all there is to it? I don't have to simplify anything? Just plug in values?

Homework Statement Why is the limit of ln(x)/arctan(x) as x approaches 0 from the right, not zero? Homework Equations The Attempt at a Solution I used L'hopital's rule and got zero. But question specifically states that is not the answer.

So for part a) I have to prove that for every h_d function, there exists a minimum? I'm not very good at proofs, so... What would I choose as the function?

Homework Statement Assume happiness can be measured on a scale from -10 (very unhappy) to 10 (extremely happy). Let D denote the set of possible ways to live one day. For each way of living a dayd∈D define a function h_d:[0,24]⟶[−10,10] to be equal to the value of happiness at each point...

$25 was the minimum? And two days other than Dec 10 can have the same stock price?

Homework Statement You know that the only time company A's stocks were traded for $25 a share was on December 10th, 2005. You also know that on June 3rd of 2001 the price was $41 a share and on September 17th of 2010 it was $34. Assuming that stock prices change continuously, what conclusion...

Homework Statement Find an f that satisfies this statement: \lim_{x\rightarrow a} f(x)≠L ∀ε>0 ∃δ>0∃ x:0<|x-a|<δ AND |f(x)-L|<ε Homework EquationsThe Attempt at a Solution I'd just like a small hint on how I would go about finding a function. How can there be a delta for every epsilon and...

Is this right? So I have: 1. \lim_{x\rightarrow 1} \cos(arctan({\frac{\sin(x-1)}{x-1}})) 2. \lim_{x\rightarrow 1} \cos(arctan({\frac{\sin(u)}{u}})) 3. \lim_{x\rightarrow 1} \cos(arctan(1)) because of the theorem: \lim_{x\rightarrow 0}({\frac{\sin(x)}{x}}))=1...

Homework Statement Use theorems to find the limit: \lim_{x\rightarrow 1} \cos(arctan({\frac{\sin(x-1)}{x-1}})) Homework Equations Theorems like f(x)=c is continuous f(x)=x is continuous \lim_{x\rightarrow 0} \cos(x)=1 \lim_{x\rightarrow 0} \sin(x)=0...

If I were to calculate the probability of getting 6 out of 6 numbers correct in a lottery where you choose six numbers out of 49 (the lottery is called 6/49), the probability would be (6C6)(43C0)/(49C6), right? But what are different methods of getting this same answer without using combinations?

This is not a specific question, but if an equation was given and you were told that f(4)= 2f(2), how would you find f(8)?

Homework Statement What effect will the tangential component of force have on the velocity of the planet? What effect will the normal component of force have on the velocity of the planet? Homework Equations The Attempt at a Solution 1. Since it is parallel to the direction of velocity, maybe...