3 for the quantum mechanical simple harmonic oscillator...

Transcript

00:01 Hello students in this question we have to show that the minimum energy for quantum harmonic oscillator is equals to enon equals to h bar omega divided so first let's see with the energy of a quantum harmonic oscillator is so the formula for energy of harmonic quantum harmonic quantum harmonic equals to del p squared dem divided by two times plus half and omega square where dlx is the position and set 20 okay so the minimum energy we have to calculate so we'll write it as delx times del p now according to has involved principle of unsaid dandy we can del x times del p now this is equal to h bar divided by two okay so we have to kind of value so to calculate the minimum of energy we can write the different sheet we can differentiate this value this equation right here with del x okay so we have to convert the value of this del p in del x so we can write the value of del p as a equal h bar divided by two del x okay so we have to write this value in this position from here e will be equal to x square divided by 4m dlex plus m omega square so this equation is converted into del x okay so we have to calculate the amountage of e so we'll apply the formula to calculate minima so to calculate the minimum of this energy will differentiate it with del x and it will come out to be d e divided by d del x now this will be equal to here we have del x in the denominator so this will be equal to del x raised to the bar minus 2 so we'll multiply the power bed as minus times here we have hs 1 divided by 4m del x raised to the power 2 okay sorry 3 we have 2 and here we will have plus m omega square times the derivation of a derivative this will be equal to del x now this is equals to zero so when when we put this value as equal to zero from here the value of del x will be equal to root h bar divided by 2m omega okay so when the value of delx is equals to this the value of energy will be minima okay so we'll write the value of del x is this in this equation so the equation of energy is e equals to hbore squared by 4m and here we write the value of del x square as h bar now multiply the denominator by the denominator as 2 m omega plus here we have half m omega times h bar divided by 2m omega okay from here the value of energy will be equal to now this will cancel out by 2 this h cans up by this h and here we have m omega okay so at the top we have h bar times omega divided by 2 plus h bar omega divided by 4 okay so we have to calculate the minimum energy now here we also have 4 so this energy e knot will be equal to h bar omega divided by two hence showed...

Question

3. For the quantum mechanical simple harmonic oscillator, verify explicitly that dC

Question

3. For the quantum mechanical simple harmonic oscillator, verify explicitly that dC

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