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I asked a question Is the average position for the ground state of a 1D simple harmonic oscillator zero?. I asked why the average position of the ground state of a simple harmonic oscillator (SHO) is not zero. And what is the meaning that the position is not zero? That is absolutely a question helping me to complete the physical concept in my mind.

To let others clearly know why I claimed the average position of the ground state of a SHO is not zero. I provided my proof.

According to my experience, I feel my question is easily be marked as "homework-like" and "check-my-work", so I tag my question as "homework". Evenly, it is not homework and I didn't ask others to check my work.

However, my question is still closed due to "homework-like" and "check-my-work". I guessed the reason is the answer pointed me out that a|0> is 0 not |0> (In fact, "a|0> is 0 not |0>" is a physical concept). Before I got the answer, I didn't know, it was unfair to say I wanted to others to "check my work".

I always introspect after my question was closed because closing my question makes me feel I am wrong. I think if I hadn't listed those equations showing how I derived the average position, voters will not feel my question was "check-my-work". But I don't think skipping equations is better. For people answering the question, more details more confidence.

Could you show me how to ask that question so that the question will not be closed as "homework-like" or "check-my-work"?

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    $\begingroup$ With all due respect, how can this not be “check-my work”, since you are basically asking where to find your error in trying to “prove the claim in the textbook is correct when $n>1$”? Alternatively, how is this NOT an assignment-like question on the action of $a$ and $a^\dagger$? $\endgroup$
    – ZeroTheHero
    Dec 31, 2022 at 18:00
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    $\begingroup$ Have you done due diligence? For instance this question (or any of the multitude of related questions on this site)? The action of $a$ and $a^\dagger$ is covered in every textbook on quantum mechanics... $\endgroup$
    – ZeroTheHero
    Dec 31, 2022 at 18:10
  • $\begingroup$ How can I know the problem was my application of ladder operators before I got the answer? If I know I need to find this question, I won't need to post the question. I know many textbooks contain the application, but I am not ChatGPT. Can you trust that I spent a reasonable time (hours) finding resources before posting the question? Please. $\endgroup$
    – IvanaGyro
    Dec 31, 2022 at 18:20
  • $\begingroup$ I think it's clear in my question. I was asking "why the average position is not zero." I did research and didn't know why it can be non-zero. $\endgroup$
    – IvanaGyro
    Dec 31, 2022 at 18:22
  • $\begingroup$ "This is weird. The wave function of the ground state of a 1D SHO is an even function in the position, so the average position should be zero." This is the information I got from my research. I did everything I could do then. $\endgroup$
    – IvanaGyro
    Dec 31, 2022 at 18:25
  • $\begingroup$ The textbook shows how to apply the ladder operator but not the derivation of the case of the ground state. That's why I tried myself and why I can't find the exact answer by reading the textbooks. $\endgroup$
    – IvanaGyro
    Dec 31, 2022 at 18:28
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    $\begingroup$ it's your job to find where the problem is... this is why it's a "check-my-work" question: because you are asking the community to do your job for you. $\endgroup$
    – ZeroTheHero
    Dec 31, 2022 at 20:55
  • $\begingroup$ You can also claim that "it's OP's job to find where the problem is" for every question. I have done my job but you didn't believe me. $\endgroup$
    – IvanaGyro
    Jan 1 at 0:39

1 Answer 1

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The OP asks why the question is considered "check-my-work" as it was closed as a result.

This is an extremely specific calculation, and the OP is stuck trying to find an error in the evaluation of $a\vert 0\rangle$. This is exactly the kind of question that defines check my work.

The lack of elementary due diligence means this question has limited reach beyond the specific answer to the OP. A simple Google search site:physics.stackexchange.com creation operator will yield multiple similar questions and it is difficult to believe the OP even bothered to check answers on this site to such questions before posting their own question.

To improve, the question should (IMO) at least be asked for any $n$, i.e., something like:

The average value of $x$ for any harmonic oscillator eigenstate is $0$ by parity. Yet, when I compute $\langle x\rangle$ using $a$ and $a^\dagger$, I get $$ a^\dagger \vert n\rangle = [\text{something}]\, ,\quad a\vert n\rangle = [\text{something else}]\, . \tag{1} $$ with the result that $\langle n\vert x\vert n\rangle \sim \langle n\vert a+a^\dagger \vert n\rangle\ne 0$ using Eq.(1) and orthogonality $\langle n\vert n+\pm 1\rangle=0$. Clearly I cannot reconcile the result using bra–ket with the physical result that should be 0. Therefore...

I'm sorry to say that this kind of question - at least as it is currently phrased - should IMO never be reopened and in fact should be quickly closed. I am but one voice, yet I do not see how this kind of question is helpful to the site. Again, IMO, the question in its current form does not bring much to anyone interested in a better understanding of the action of creation and destruction operator because of its specificity, except possibly for a student who is faced with an assignment question where they need to evaluate $a\vert 0\rangle$ or $a^\dagger \vert 0\rangle$.

I do hope others will include their suggestions on how to improve this question.

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  • $\begingroup$ "The OP is stuck trying to find an error in the evaluation of a|0⟩" is wrong. The OP believed a|0⟩ is |0⟩. If "the OP is stuck trying to find an error in the evaluation of a|0⟩" is true, I can accept the question as a "check-my-work" question, but it's not. Thank you for providing an improvement example, however, I don't see any extra information that the OP didn't provide in the question. 1. using operator - provided 2. ⟨n|x|n⟩∼⟨n|a+a†|n⟩≠0 - provided 3. orthogonality - provided 4. physical result that should be 0 - provided 5. asking concept about non-zero result - provided $\endgroup$
    – IvanaGyro
    Jan 1 at 0:47
  • $\begingroup$ I saw you were one of the people close to the question. Can you provide a full question example in my context? I will try if it will not be closed. $\endgroup$
    – IvanaGyro
    Jan 1 at 0:48
  • $\begingroup$ According to this answer, I think you totally misunderstood what OP asked. $\endgroup$
    – IvanaGyro
    Jan 1 at 0:50
  • $\begingroup$ Didn’t I do just that with the bit in italics? And what part did I misunderstand in the OP? You write $a\vert 0\rangle=\vert 0\rangle$, which is where the error is…. Of course as there is no additional detail it’s not possible to understand why you write this… $\endgroup$
    – ZeroTheHero
    Jan 1 at 2:48
  • $\begingroup$ You thought "the OP is stuck trying to find an error in the evaluation of a|0⟩". This is the point you misunderstood the context. See the title of that question. The title is the question what OP asked. $\endgroup$
    – IvanaGyro
    Jan 1 at 9:36
  • $\begingroup$ The additional detail is necessary as you mentioned. But the reason you tagged the question "check-my-work" related to the additional details doesn't it? If there is no additional details, you will not feel "the OP is stuck trying to find an error in the evaluation of a|0⟩". $\endgroup$
    – IvanaGyro
    Jan 1 at 9:40
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    $\begingroup$ look…. This is not constructive. My evaluation is that you are so confused that you cannot even phrase your confusion clearly. The remedy for this is to stop, take some time (days) to study sources (plural) other than the ones you are using now, and beef up your background. I really hope my assessment is incorrect but that’s how your questions currently come across. If you continue to use this site to ask for check-my-work questions, they will be closed and you will eventually get in trouble, and that’s not useful for anyone. $\endgroup$
    – ZeroTheHero
    Jan 1 at 14:59
  • $\begingroup$ You used a deconstructive way to implement your ideology on a public forum and said others are not constructive. What is constructive? Closing questions by guessing others' intentions or adding content on the Internet? I am a student now, but I am not young. You don't know whether your life or my life is more successful. I never use patriarchy-like language to tell others to go study. You will never know if a question will help anyone in the future. You are not a time traveller. I don't know how to not ask a check-my-work question because someone is defining check-my-work question. $\endgroup$
    – IvanaGyro
    Jan 1 at 15:41
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    $\begingroup$ That escalated quickly. $\endgroup$
    – Tobias Fünke
    Jan 1 at 16:50
  • $\begingroup$ @TobiasFünke There's good will on both sides (at least I hope) so this will pass. $\endgroup$
    – ZeroTheHero
    Jan 1 at 16:52
  • $\begingroup$ Just my two cents: I also cannot believe that if OP checked some sources (intro books or lecture notes for quantum mechanics) that they did not encountered at one occasion that $a|0\rangle = 0$ holds...Yet, this is possible, of course. But then the question still appears as if OP did not do enough research. $\endgroup$
    – Tobias Fünke
    Jan 1 at 17:00
  • $\begingroup$ @TobiasFünke the difficulty is that it's not clear if $a\vert 0\rangle=0$ is where the issue is since the OP provided no details at all on how they understand the action of $a$ on $\vert n\rangle$. Well.. it is what it is... $\endgroup$
    – ZeroTheHero
    Jan 1 at 17:11
  • $\begingroup$ As the idiot who answered the question, that was a bit of a snafu on my end. I'd already written what was there before I realized I'd answered a similar query before (linked in my comments there), but when my wife told me a few minutes later that she was in labor (another girl born 60 minutes later!), I must've hit the submit button when trying to close out, so oops. $\endgroup$
    – Kyle Kanos
    Jan 3 at 19:43
  • $\begingroup$ @KyleKanos we can all agree your personal circumstances are in this case sufficient to excuse you snafu. I do hope mother and daughter are well! Congrats! $\endgroup$
    – ZeroTheHero
    Jan 3 at 20:39
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    $\begingroup$ @ZeroTheHero Everyone is doing well, thanks! $\endgroup$
    – Kyle Kanos
    Jan 4 at 20:19

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