بررسي اثر تابع ويژه در مقدار چشم داشتي كميات فيزيكي يك ذره در يك چاه پتانسيل دوگانه متقارن

Effect of Eigenfunction on the Expectation Values of Different Physical Parameters for a Particle in a Double Well Potential

ﺣﻞ ﻣﺴﺎﺋﻞ ﻣﮑﺎﻧﯿﮏ ﮐﻮاﻧﺘﻮﻣﯽ ﻧﯿﺎز ﺑﻪ ﺣﻞ ﻣﻌﺎدﻟﻪ ﺷﺮودﯾﻨﮕﺮ دارد ﮐﻪ در آن ﻣﻘﺎدﯾﺮ وﯾﮋه و ﺗﻮاﺑﻊ وﯾﮋه ﺑﺴﺘﮕﯽ ﺑﻪ ﭘﺘﺎﻧﺴﯿﻞ ﮐﺎرﺑﺮدي دارﻧﺪ. ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﻫﻤﯿﺖ ﻣﻮﺿﻮع در اﯾﻦ ﻣﻘﺎﻟﻪ ﮐﻤﯿﺎت ﻓﯿﺰﯾﮑﯽ ﯾﮏ ذره ﺑﺎ اﺳﺘﻔﺎده از ﭘﺘﺎﻧﺴﯿﻞ ﭼﺎه دوﮔﺎﻧﻪ ﻣﺘﻘﺎرن ﺑﺮرﺳﯽ ﻣﯽﺷﻮﻧﺪ. در اﯾﻦ ﻣﻘﺎﻟﻪ، ﻣﻘﺎدﯾﺮ ﭼﺸﻢداﺷﺘﯽ ﺑﺎ اﺳﺘﻔﺎده از ﻧﺮم اﻓﺰار CUPS ﺑﺮرﺳﯽ ﻣﯽﺷﻮﻧﺪ و اﺛﺮ اﻧﺘﺨﺎب ﺗﻮاﺑﻊ وﯾﮋه ﻣﺨﺘﻠﻒ را ﺑﺮ روي ﮐﻤﯿﺎت ﻓﯿﺰﯾﮑﯽ ﻣﻮرد ﻣﻄﺎﻟﻌﻪ ﻗﺮار ﻣﯽدﻫﯿﻢ. در اﻧﺘﻬﺎ ﺑﻪ ﺗﻔﺴﯿﺮ ﻧﺘﺎﯾﭻ و ﻧﻘﺶ ﻫﺮ ﯾﮏ از اﯾﻦ ﭘﺎراﻣﺘﺮﻫﺎ در ﺗﻐﯿﯿﺮات ﺣﺎﺻﻞ ﺷﺪه وﺷﺮاﯾﻂ وﯾﮋه آﻧﻬﺎ ﻣﯽﭘﺮدازﯾﻢ.

in this paper, using the CUPS software the expectation value for a particle in a symmetric Double Well Potential is computed. Expectations values for different physical quantities such as position, momentum, kinetic energy, potential energy and total energy are reported for three different eigenfunctions. The effects of the eigenfunction on the computed quantities are investigated and results are compared for a better interpretation. The physical reason for the differences in the results is given for the obtained parameters. Some quantities such as expectation value of the position and momentum are insensitive to the chosen eigen- function, but parameters such as particle energy is very sensitive to the eigenfunction change. The obtained results clearly show that such a computational method is an important tool in solving quantum mechanical problems with great advantage in respect to the analytical methods.