Solve Quantum Mech Problem: Find N for Normalized Wavefunction

  • Thread starter Thread starter IanSimcox
  • Start date Start date
  • Tags Tags
    Quantum
AI Thread Summary
To find the normalization constant N for the wavefunction U(x) = N exp(-((x-y)^2)/2a^2), one must ensure that the integral of the square modulus of U(x) from negative to positive infinity equals 1. This involves calculating the integral of |U(x)|^2, which is N^2 times the integral of exp(-((x-y)^2)/a^2). The user expresses uncertainty about the normalization concept but realizes it involves integrating the square modulus. The discussion emphasizes the importance of correctly applying the normalization condition in quantum mechanics. Understanding this process is crucial for solving the homework problem effectively.
IanSimcox
Messages
2
Reaction score
0
Hi, I'm not sure this is the correct topic for this question, but I shall ask anyway.

I've been set this question for homework and I'm not too sure where to start.

Find N so that the state |U> with Schrodinger position representation wavefunction U(x) = N exp(-((x-y)^2)/2a^2) is normalised, where a and y are real constants.

Hopefully from there I will be able to do the rest of the question.
 
Physics news on Phys.org
Do you know what 'normalised' means? Look it up!
 
Ok this could make me look like an idiot either way (probably coz I'm not too sure of what I'm about to say, I should listen more), but I think it means that if I integrate U(x) from -infinte to +infinite then the answer should be 1. If it is I feel kinda silly not havin thought of doing that.
 
No,u have to integrate the square modulus...of the wave function.

Daniel.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Quantum Mechanics I, finding impuls wavefunction.
Replies
6
Views
911
Understanding a math step in solving Schrödinger's equation for single particle in a box
Replies
8
Views
916
Quantum Physics - Electron in a 1d Potential Well Question
Replies
1
Views
2K
Normalizing the Wavefunction: A Question of Integration
Replies
8
Views
2K
Finding the quantum number using Morse Potential
Replies
14
Views
3K
Confusion In Writing Identical Particle Wavefunctions
Replies
12
Views
310
Is My Quantum Well Probability Calculation Correct?
Replies
9
Views
2K
Help Calculating probability between 2 limits for the ground state
Replies
28
Views
2K
Griffiths' Quantum Mechanics Problem 4.27 : Diatomic particles
Replies
46
Views
676
What Do Coefficients and Expectation Values Mean in Quantum Mechanics?
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top