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https://texercises.com/exercise/heisenberg-uncertainty/
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Exercise:
Show that for a stationary state of the infinite potential well the uncertaies of position and momentum fulfil the Heisenberg uncertay principle sigma_xsigma_p &geq frachbar

Solution:
We have already seen that the uncertaies for position and momentum in the state psi_nxt are sigma_x L sqrtfracn^ pi^ - n^ pi^ sigma_p fracnpihbarL The product is thus sigma_xsigma_p sqrtfracn^ pi^ - n^ pi^npihbar This expression has the smallest value for n: sigma_xsigma_p sqrtfrac-fracpi^pihbar sqrtfracpi^-frachbar &approx valueP times hbar geq frachbar as predicted by the Heisenberg uncertay principle.
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Exercise:
Show that for a stationary state of the infinite potential well the uncertaies of position and momentum fulfil the Heisenberg uncertay principle sigma_xsigma_p &geq frachbar

Solution:
We have already seen that the uncertaies for position and momentum in the state psi_nxt are sigma_x L sqrtfracn^ pi^ - n^ pi^ sigma_p fracnpihbarL The product is thus sigma_xsigma_p sqrtfracn^ pi^ - n^ pi^npihbar This expression has the smallest value for n: sigma_xsigma_p sqrtfrac-fracpi^pihbar sqrtfracpi^-frachbar &approx valueP times hbar geq frachbar as predicted by the Heisenberg uncertay principle.
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quantum physics
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heisenberg, momentum, position, uncertainty
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ENG (English)
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Calculative / Quantity
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