Using Solve[] to find Eigenstates of a 1D Double Dirac Potential

I’d like to Solve

$ $ k^2 \equiv – \frac{2mE}{\hbar^2} = (- \frac{mA}{\hbar^2} (1+ e^{-2ka}))^2 $ $

for E, in terms of m, $ \hbar$ , A, a.

I tried using the following command:

Solve[-((2 m ene)/h^2) == (m^2 A^2)/h^4 (1 + E^(-2 a*Sqrt[-((2 m ene)/h^2)])), ene] 

Isn’t working well for this task. What do you recommend? At first glance it seems it could not be simple to solve "by hand".

Background: This problem comes from Solving a 1D Quantum well with 2 Symmetric Dirac’ Deltas $ \delta_a$ and $ \delta_{-a}$ , where $ A$ is the amplitude.

Find maximal subset with interesting weight function

You are given $ n$ rows of positive integers of length $ k$ . We define a weight function for every subset of given $ n$ rows as follows – for every $ i = 1, 2, \dots, k$ take the maximum value of $ i$ -th column (), then add up all the maximums.

For example, for $ n = 4$ , $ k = 2$ and rows $ (1, 4), (2, 3), (3, 2), (4, 1)$ the weight of subset $ (1, 4), (2, 3), (3, 2)$ is $ \max\{1, 2, 3\} + \max\{4, 3, 2\} = 3 + 4 = 7$ .

The question is, having $ m \leq n$ , find the subset of size $ m$ (from given $ n$ rows) with maximal weight.

The problem looks trivial when $ m \geq k$ , but how can one solve it for $ m < k$ ? Looks like dynamic programming on subsets could work for small $ k$ , isn’t it? Are there other ways to do it?

Why does the formula floor((i-1)/2) find the parent node in a binary heap?

I learned that when you have a binary heap represented as a vector / list / array with indicies [0, 1, 2, 3, 4, 5, 6, 7, 8, …] the index of the parent of element at index i can be found with parent index = floor((i-1)/2)

I have tried to explain why it works. Can anyone help me verify this?

Took reference from Why does the formula 2n + 1 find the child node in a binary heap? thanks to @Giulio

Trying to find a way to play dnd?

So, basically me and my friends wants to play dnd, but I’m in a country where its very hard to get the dnd rule books, and because of an impending lockdown I cant get them shipped to where I am. I’ve played the game a few times and have followed a few campaigns on twitch/youtube so I’m familiar with the basic rules. But, I wanna know if anyone here has any advice as to how I would practically get a game started up.

(worth noting that internet access is fairly limited and is also completely unavailable)

Preferably, I’d like to play 5e. If there’s an easier one I would obviously be open to suggestions

How to find and evaluate anonymizing remailers?

Following this post:

Anonymized posting mechanism for members-only-post mailing lists

I’m interested in an anonymous remailer which makes emails appear to originate in a fixed address (which would be allowed to post to a certain mailing list). Now, I’ve read the Wikipedia article on these remailers; and it seems like what I need is the use of a pseudonym + removal of "Received:" headers up to the remailer.

My question is, how can I find (free) remailers which offer this feature? And is there a way to verify they really offer it other than by starting to use them? So far, I’ve found mostly dead links and/or opaque systems with a web form.

Notes: I’m not interested into ultra-secure government-wiretapping-resistant remailer. Just something that a typical knowledgeable person would not be able to trace back to the real author. What I do need to be able to do is send (not-huge) attachments.

find the vector v

Chef John is given N points P1,P2,…,PN in a plane. For each valid i, the coordinates of the point Pi are (xi,yi). Help him find a vector v→=(xv,yv) such that the following holds:

For each i (1≤i≤N), let Si=v→⋅PiPi+1. Here, we define Pn+1=P1. The coordinates xv and yv are integers and |xv|,|yv|≤2⋅109. It is possible to find three integers w, l and r (1≤l≤r≤N) such that: For each i (l≤i≤r), Siw>0. For each other valid i, Siw<0. If there are multiple solutions, you may find any one. If there are no solutions, let’s define xv=yv=0. (Note that the vector v→=(0,0) cannot be a valid solution.)

With respect to differential privacy how to find the global sensitivity of queries like ‘maximum height’ ‘Average height’ etc

As much as I have understood,for any query f(x), we need to take maximum of |f(x)-f(y)| over all neighboring databases.

please explain how to find global sensitivity of queries like average height or maximum height.

Find the maximum number of valid cartesian coordinates

Given a list X containing m number of x coordinates and a list Y containing m number of y coordinates. The coordinate (x, y) is valid if and only if the difference between x and y is less than or equal to d. I need to find out the maximum number of valid coordinates. Here is my algorithm.

sort the list X in non-decreasing order sort the list Y in non-decreasing order for x in X:      for y in Y:          if abs(x - y) <= d:              let x match with y              remove x from X              remove y from Y 

Can this algorithm give me maximum number of valid pairs? If yes, is there any more efficient algorithm? The nested loop means the worst-case time is $ O(m^2)$ . Is there any log linear time $ O(mlogm)$ algorithm for this question?

Where can I find experiential-based resources for West Marches/Open Table games?

I’m currently getting ready to run an Open Party/West Marches style game with a pool of about 16 players. We’ll be using 5e, but my question is system-agnostic.

I of course started with Ben Robbins’ "Grand Experiments: West Marches" blog posts (here: ), but after reading those and Justin Alexander’s "Open Table Manifesto" I’m having a tough time finding anything else experiential. Pretty much every other resource I find references one of those two to define the playstyle, says they think it’s a neat idea they’d like to try, and stops there.

I can’t say I’m shocked; building a sandbox like this is a lot of work and I don’t know that I’d want to go to the trouble of annotating it for strangers on the internet. It’s almost shocking that it’s happened twice.

That being said, I’m specifically looking for things similar to Ben’s West Marches: Running Your Own where a GM who has actually run an Open Party/West March style game for some time gives experience-based advice.

Of highest import is anything that gives insight on managing in-game vs. real-world time with multiple parties.