The discussion revolves around determining the ground state of a particle with mass 'm' in a potential described by V(x) = x^2, which is related to the quantum harmonic oscillator model.
Participants are actively engaging with the problem, with some providing guidance on the relationship to the harmonic oscillator. There is acknowledgment of the need to understand the problem thoroughly, suggesting a productive direction in the discussion.
There is an emphasis on ensuring a foundational understanding of the problem, as indicated by a participant's reminder to approach it from scratch. This suggests a focus on learning rather than simply arriving at an answer.
[itex] <br /> It looks good (Of course, n=0 for the ground state, don't forget that!), but make sure you know how to do the problem from scratch. I'm guessing that's what your professor wanted you to do.<br /> <br /> -Dan[/itex]Reshma said:Thanks, inha! I compared it to the PE function of a harmonic oscillator.
[tex]V(x) = {1\over 2} m \omega^2 x^2[/tex]
Comparing it with [itex]V(x) = x^2[/tex],<br /> <br /> [tex]{1\over 2} m \omega^2 = 1[/tex]<br /> <br /> [tex]\omega = \sqrt{2\over m}[/tex]<br /> <br /> And I substitute this value in the formula:<br /> [tex]E_n = \hbar \omega \left(n + {1\over 2}\right)[/tex]<br /> <br /> Am I going right? <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f615.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":confused:" title="Confused :confused:" data-smilie="5"data-shortname=":confused:" />[/itex]