Physics Help Forum particle (infinite 1-D well)

 Nuclear and Particle Physics Nuclear and Particle Physics Help Forum

 Nov 14th 2014, 02:19 PM #1 Junior Member   Join Date: Oct 2014 Posts: 12 particle (infinite 1-D well) The problem statement, all variables and given/known data If a particle (infinite 1-D well) in ground state n =1 with an energy 1.26 eV above E=0. Whats the energy needed to get it to 3rd excited state n =4? any hints?
Nov 14th 2014, 03:00 PM   #2

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 Originally Posted by mss90 The problem statement, all variables and given/known data If a particle (infinite 1-D well) in ground state n =1 with an energy 1.26 eV above E=0. Whats the energy needed to get it to 3rd excited state n =4? any hints?
The energy of a particle in an infinite square well potential (V = 0 from x = 0 to x = a) is
E = [pi ^2 hbar^2 / (2 m a^2)] n^2

You can use this for n = 1, E = 1.26 eV to find a.

-Dan
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 Nov 15th 2014, 08:47 AM #3 Junior Member   Join Date: Oct 2014 Posts: 12 whats the name of that formula? thanks
 Nov 15th 2014, 01:48 PM #4 Junior Member   Join Date: Oct 2014 Posts: 12 Did you mean En = h2kn2/(2m) or En = n2π2ħ2/(2mL2)? I got a=(pi^2 ħ^2/E2m)*1^2 where ħ=h/2pi a=1.66E-34/2.3E-30 a= 7.22E-5eV Last edited by mss90; Nov 15th 2014 at 02:03 PM.
Nov 15th 2014, 02:05 PM   #5

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 Originally Posted by mss90 Did you mean En = h2kn2/(2m) or En = n2π2ħ2/(2mL2)? Whats ħ anyways?
The second expression is correct. I used "a" for the width of the square well, whereas you used "L."

The Schrodinger equation is a "eigenvalue" equation. E is the energy eigenvalue for a particle in a state with "n" equal to some (quantized) number.

How can you not know what hbar is?? hbar is defined as Planck's constant divided by 2 pi.

How can you even ask these questions? You had to solve the Schrodinger equation to get to this point!

-Dan
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 Nov 15th 2014, 02:10 PM #6 Junior Member   Join Date: Oct 2014 Posts: 12 Why should I know that, I havnt learned it anywhere.. I removed it from the question as i managed to find it online. No I havnt solved schrodinger equation, and I found the formula online.
 Nov 15th 2014, 02:16 PM #7 Junior Member   Join Date: Oct 2014 Posts: 12 so if i just got the width of the well, how do i go about finding the energy needed to get it to 3rd excited state n =4
Nov 15th 2014, 04:18 PM   #8

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 Originally Posted by mss90 so if i just got the width of the well, how do i go about finding the energy needed to get it to 3rd excited state n =4
Just plug n = 4 into the energy equation I posted.

I'm curious. How can you be expected to solve the problem of an infinite square well if you haven't covered the Schrodinger equation? This makes no sense to me at all.

-Dan
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 Nov 16th 2014, 06:24 AM #9 Junior Member   Join Date: Oct 2014 Posts: 12 like this -> E4=(1.66E-34/(2m*7.22E-52))*42 E4=1.6E27eV? well it has been covered briefly but i didnt learn it. To be honest I never expected there to be this much maths and physics in the degree im doing. I havnt done physics and maths in almost 4 years now and no previous knowledge in them were required. Hence Im not sure If ill manage. I appreciate you assisting me tho
 Nov 16th 2014, 10:53 AM #10 Forum Admin     Join Date: Apr 2008 Location: On the dance floor, baby! Posts: 2,780 You have an energy level of 1.5 x 10^{27} eV?? Ouch! Any electron orbital energies will be in the eV range, not 10^{27} eV. Two things first: Notation. "42" is a number. It is not 16. When writing exponents please use "^" ie 4^2. Second: I can help you but I can't really teach you on the Forum. You really need to talk to your instructor about these things. Okay. We don't yet know m or L. So I'm going to go for broke and solve E_n = (hbar^2 Pi^2) n^2/ (2mL^2) for 2mL^2: 2mL^2 = (hbar^2 Pi^2) n^2 / E_n We are given n =1, E_1 = 1.26 eV, which gives: 2mL^2 = 3.39348 x 10^{-30} Now we can use that for n = 4: E_n = (hbar^2 Pi^2) n^2/ (2mL^2) E_4 = (hbar^2 Pi^2 * 4^2) / 3.39348 x 10^{-30} = 20.16 eV. If you do a few of these you will notice that E_n = E_1 * n^2. -Dan __________________ Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup. See the forum rules here. Last edited by topsquark; Nov 16th 2014 at 10:55 AM.

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