ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ

ᱞᱟᱹᱣᱠᱟᱹ ᱠᱟᱹᱢᱤ ᱨᱮᱭᱟᱜ ᱤᱞᱮᱠᱴᱨᱚᱱ ᱦᱟᱭᱰᱨᱚᱡᱮᱱ ᱮᱴᱚᱢ ᱨᱮ ᱵᱷᱮᱜᱟᱨ ᱫᱟᱲᱮ ᱛᱷᱟᱠ᱾ ᱩᱱᱠᱩ ᱫᱚ ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱞᱮᱠᱟᱛᱮ ᱯᱞᱚᱴ ᱟᱠᱟᱱᱟ ᱠᱚ᱾

ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱫᱚ ᱠᱣᱟᱱᱴᱚᱢ ᱢᱮᱠᱟᱱᱤᱠ ᱨᱮ ᱢᱤᱫ ᱢᱩᱞᱦᱚᱸᱫ ᱥᱚᱢᱟᱱ ᱠᱟᱱᱟ ᱚᱠᱟ ᱫᱚ ᱵᱮᱣᱨᱟ ᱮᱢᱚᱜ ᱠᱟᱱᱟ ᱡᱮ ᱚᱠᱛᱚ ᱥᱟᱶ ᱥᱟᱶᱛᱮ ᱯᱷᱤᱡᱤᱠᱟᱞ ᱥᱤᱥᱴᱚᱢ ᱨᱮᱭᱟᱜ ᱠᱣᱟᱱᱴᱚᱢ ᱚᱵᱚᱥᱛᱟ ᱪᱮᱫ ᱞᱮᱠᱟ ᱵᱚᱫᱚᱞᱚᱜ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱫᱚ ᱚᱥᱴᱨᱤᱭᱟᱱ ᱯᱷᱤᱡᱤᱥᱤᱥᱴ ᱮᱨᱣᱤᱱ ᱥᱠᱨᱳᱰᱤᱝᱜᱟᱨ, ᱟᱜ ᱧᱩᱛᱩᱢ ᱛᱮ ᱧᱩᱛᱩᱢ ᱟᱠᱟᱱᱟ ᱚᱠᱚᱭ ᱫᱚ ᱱᱚᱣᱟ ᱑᱙᱒᱕ ᱨᱮ ᱛᱮᱭᱟᱨ ᱞᱮᱫᱟᱭ᱾

ᱯᱮ ᱰᱟᱭᱢᱮᱱᱥᱚᱱᱟᱞ ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱞᱟᱹᱜᱤᱫ ᱢᱤᱫ ᱠᱟᱱᱰᱤ ᱞᱟᱹᱜᱤᱫ ᱵᱮᱜᱚᱨ ᱚᱠᱛᱚ ᱞᱮᱛᱟᱲ ᱵᱮᱜᱚᱨ ᱛᱮ ᱥᱟᱝᱜᱷᱟᱨ ᱨᱮ ᱪᱟᱞᱟᱜ ᱠᱟᱱᱟᱭ:

$-{\frac {\hbar ^{2}}{2m}}{\frac {\partial ^{2}}{\partial x^{2}}}\Psi (x,\,t)+V(x)\Psi (x,t)=i\hbar {\frac {\partial }{\partial t}}\Psi (x,\,t)$

ᱚᱠᱛᱚ ᱯᱷᱩᱨᱜᱟᱹᱞ ᱥᱠᱨᱳᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱫᱚ ᱢᱚᱴᱟ ᱞᱮᱠᱟᱛᱮ ᱞᱟᱛᱟᱨ ᱨᱮ ᱮᱢ ᱟᱠᱟᱱ ᱵᱟᱨ ᱵᱷᱮᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱞᱮᱠᱟ ᱵᱚᱨᱱᱚᱱ ᱟᱠᱟᱱᱟ:

$i\hbar {\frac {dT(t)}{dt}}=E\,T(t)$

$-{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi (x)}{dx^{2}}}+V(x)\psi (x)=E\,\psi (x)$

ᱥᱠᱨᱳᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱫᱚ ᱟᱭᱢᱟ ᱯᱟᱦᱴᱟ ᱠᱚ ᱥᱮᱞᱮᱫ ᱢᱮᱱᱟᱜᱼᱟ, ᱡᱟᱦᱟᱸ ᱨᱮᱺ

1. ᱣᱮᱵᱽᱯᱷᱟᱱᱥᱚᱱ: ᱠᱣᱟᱱᱴᱚᱢ ᱢᱮᱠᱟᱱᱤᱠ ᱨᱮ, ᱥᱤᱥᱴᱚᱢ ᱨᱮᱭᱟᱜ ᱚᱵᱚᱥᱛᱟ ᱫᱚ ᱣᱮᱵᱷᱯᱷᱟᱱᱥᱚᱱ ᱧᱩᱛᱩᱢᱟᱱ ᱮᱞᱠᱷᱟ ᱡᱤᱱᱤᱥ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣ ᱟᱠᱟᱱᱟ, ᱚᱠᱟ ᱫᱚ ᱜᱽᱨᱤᱠ psi (Ψ) ᱪᱤᱠᱤ ᱛᱮ ᱩᱫᱩᱜ ᱟᱠᱟᱱᱟ᱾ ᱣᱮᱵᱽ ᱯᱷᱟᱱᱥᱚᱱ ᱨᱮ ᱥᱤᱥᱴᱚᱢ ᱨᱮᱭᱟᱜ ᱜᱩᱱ ᱠᱚ ᱵᱟᱵᱚᱛ ᱥᱟᱱᱟᱢ ᱵᱟᱯᱟᱰᱟᱭ ᱛᱟᱦᱮᱱᱟ, ᱡᱮᱞᱠᱟ ᱫᱷᱟᱯ, ᱜᱷᱟᱹᱲᱤ ᱟᱨ ᱫᱟᱲᱮ᱾

2. ᱚᱠᱛᱚ ᱩᱛᱱᱟᱹᱣ: ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱞᱟᱹᱭ ᱟᱵᱚᱱᱟᱭ ᱪᱮᱫ ᱞᱮᱠᱟ ᱚᱠᱛᱚ ᱥᱟᱶ ᱥᱟᱶᱛᱮ ᱱᱚᱣᱟ ᱣᱮᱵᱷᱯᱷᱟᱱᱥᱚᱱ ᱩᱛᱱᱟᱹᱣᱚᱜ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱫᱚ ᱢᱤᱫ ᱡᱚᱢᱟᱜ ᱞᱮᱠᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱥᱤᱥᱴᱚᱢ ᱨᱮᱭᱟᱜ ᱱᱟᱦᱟᱜ ᱚᱵᱚᱥᱛᱟ ᱦᱟᱛᱟᱣ ᱠᱟᱛᱮ ᱞᱟᱹᱭ ᱟᱢᱟ ᱟᱜᱟᱢ ᱨᱮ ᱱᱚᱣᱟ ᱪᱮᱫ ᱞᱮᱠᱟ ᱧᱮᱞᱚᱜᱼᱟ᱾

3. ᱮᱞᱠᱷᱟ ᱨᱩᱯ: ᱥᱚᱢᱟᱱ ᱫᱚ ᱵᱟᱨ ᱨᱩᱯ ᱨᱮ ᱦᱤᱡᱩᱜᱼᱟ:

• ᱚᱠᱛᱚ ᱞᱮᱠᱟᱛᱮ ᱥᱠᱨᱳᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱᱺ ᱱᱚᱣᱟ ᱯᱷᱚᱨᱢ ᱫᱚ ᱵᱚᱨᱱᱚᱱ ᱮᱢᱟᱭᱟ ᱪᱮᱫ ᱞᱮᱠᱟ ᱚᱠᱛᱚ ᱥᱟᱶ ᱛᱮ ᱣᱮᱵᱷᱯᱷᱟᱱᱥᱚᱱ ᱵᱚᱫᱚᱞᱚᱜ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱨᱮ ᱫᱟᱲᱮ ᱨᱮᱭᱟᱜ ᱫᱷᱟᱨᱱᱟ (ᱦᱟᱢᱤᱞᱴᱚᱱᱤᱭᱟᱱ ᱚᱯᱨᱮᱴᱚᱨ ᱦᱚᱛᱮᱛᱮ) ᱟᱨ ᱩᱭᱦᱟᱹᱨ ᱭᱩᱱᱤᱴ (i) ᱥᱮᱞᱮᱫ ᱢᱮᱱᱟᱜ-ᱟ, ᱚᱠᱟ ᱫᱚ ᱠᱣᱟᱱᱴᱚᱢ ᱠᱟᱱᱰᱤᱠᱚ ᱨᱮᱭᱟᱜ ᱞᱟᱲᱦᱟᱭ ᱞᱮᱠᱟᱱ ᱯᱨᱚᱠᱨᱤᱛ ᱮ ᱩᱫᱩᱜᱟ᱾

• ᱚᱠᱛᱚ ᱯᱷᱩᱨᱜᱟᱹᱞ ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ: ᱱᱚᱣᱟ ᱨᱩᱯ ᱫᱚ ᱚᱱᱠᱟᱱ ᱥᱤᱥᱴᱚᱢ ᱞᱟᱹᱜᱤᱫ ᱵᱮᱵᱷᱟᱨᱚᱜ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱨᱮ ᱫᱟᱲᱮ ᱫᱚ ᱚᱠᱛᱚ ᱥᱟᱶ ᱵᱟᱝ ᱵᱚᱫᱚᱞᱚᱜᱼᱟ, ᱡᱮᱢᱚᱱ ᱮᱴᱚᱢ ᱨᱮ ᱤᱞᱮᱠᱴᱨᱚᱱ᱾ ᱱᱚᱣᱟ ᱟᱞᱮ ᱜᱚᱲᱚ ᱮᱢᱟ ᱞᱮᱭᱟ ᱥᱚᱢᱵᱷᱚᱵᱚᱱ ᱫᱟᱲᱮ ᱛᱷᱟᱠ (ᱵᱟᱝᱠᱷᱟᱱ ᱚᱵᱚᱥᱛᱟ) ᱥᱤᱥᱴᱚᱢ ᱨᱮ ᱛᱟᱦᱮᱸ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ᱾

4. ᱥᱚᱢᱵᱷᱚᱵᱚᱱᱟ: ᱣᱮᱵᱽ ᱯᱷᱟᱱᱥᱚᱱ ᱫᱚ ᱚᱱᱟ ᱵᱟᱝ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱫᱚ ᱟᱵᱚ ᱥᱚᱡᱷᱮ ᱵᱚᱱ ᱡᱚᱠᱷᱟ ᱫᱟᱲᱮᱭᱟᱜᱼᱟ᱾ ᱚᱱᱟ ᱵᱚᱫᱚᱞ ᱛᱮ, ᱱᱚᱣᱟ ᱨᱮᱭᱟᱜ ᱯᱩᱨᱟᱹ ᱜᱚᱱᱚᱝ (|Ψ|2) ᱨᱮᱭᱟᱜ ᱵᱚᱨᱟᱵᱚᱨ ᱫᱚ ᱢᱤᱫ ᱴᱮᱱ ᱚᱵᱚᱥᱛᱟ ᱥᱮ ᱴᱷᱟᱶ ᱨᱮ ᱠᱟᱱᱰᱤ ᱧᱟᱢ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱚᱵᱚᱱᱟ ᱰᱮᱱᱥᱤᱴᱤ ᱮᱢᱚᱜ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱥᱚᱢᱵᱷᱚᱵᱚᱱᱟ ᱥᱤᱨᱡᱚᱱ ᱫᱚ ᱠᱣᱟᱱᱴᱚᱢ ᱢᱮᱠᱟᱱᱤᱠ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱢᱩᱬ ᱜᱩᱱ ᱠᱟᱱᱟ᱾

5. ᱮᱯᱞᱤᱠᱮᱥᱚᱱ: ᱥᱠᱨᱚᱰᱤᱝᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱫᱚ ᱢᱟᱭᱠᱚᱥᱠᱚᱯᱤᱠ ᱫᱷᱟᱯ ᱨᱮ ᱠᱟᱱᱰᱤᱠᱚ ᱨᱮᱭᱟᱜ ᱵᱮᱵᱷᱟᱨ ᱞᱟᱹᱜᱤᱫ ᱵᱮᱵᱚᱦᱟᱨᱚᱜ ᱠᱟᱱᱟ, ᱡᱮᱞᱮᱠᱟ ᱮᱴᱚᱢ ᱨᱮ ᱤᱞᱮᱠᱴᱨᱚᱱ, ᱟᱹᱱᱩ ᱟᱨ ᱢᱟᱨᱟᱝ ᱥᱤᱥᱴᱚᱢ ᱨᱮ ᱦᱚᱸ᱾ ᱱᱚᱣᱟ ᱟᱵᱚ ᱠᱮᱢᱤᱠᱮᱞ ᱵᱚᱱᱰᱤᱝ, ᱠᱣᱟᱱᱴᱚᱢ ᱴᱟᱱᱮᱞᱤᱝ ᱟᱨ ᱡᱤᱱᱤᱥ ᱠᱚ ᱨᱮᱭᱟᱜ ᱜᱚᱦᱚᱲ ᱵᱩᱡᱷᱟᱹᱣ ᱞᱟᱹᱜᱤᱫ ᱜᱚᱲᱚ ᱮᱢᱟ ᱵᱚᱱᱟ᱾

ᱠᱷᱟᱴᱚ ᱛᱮ, ᱥᱠᱨᱚᱰᱤᱱᱜᱟᱨ ᱥᱚᱢᱟᱱ ᱫᱚ ᱠᱷᱟᱱᱴᱚᱢ ᱢᱮᱠᱟᱱᱤᱠ ᱨᱮᱭᱟᱜ ᱢᱚᱱᱮ ᱠᱟᱱᱟ, ᱚᱱᱟ ᱫᱚ ᱥᱚᱢᱵᱷᱚᱵᱚᱱ, ᱞᱟᱲᱦᱟᱭ ᱞᱮᱠᱟᱱ ᱯᱨᱚᱢᱚᱣᱟᱨᱠ ᱨᱮ ᱠᱟᱱᱰᱤᱠᱚ ᱨᱮᱭᱟᱜ ᱵᱮᱵᱷᱟᱨ ᱞᱮᱠᱷᱟ ᱟᱨ ᱩᱭᱦᱟᱹᱨ ᱨᱮᱭᱟᱜ ᱰᱟᱦᱟᱨ ᱮᱢᱚᱜ ᱠᱟᱱᱟ᱾ ᱱᱚᱣᱟ ᱫᱚ ᱠᱣᱟᱱᱴᱚᱢ ᱛᱷᱤᱭᱚᱨᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱟᱱ ᱮᱞᱠᱷᱟ ᱟᱨ ᱵᱷᱟᱹᱣᱛᱤᱠ ᱡᱮᱜᱮᱛ ᱨᱮ ᱧᱮᱞᱚᱜ ᱜᱷᱚᱴᱱᱟ ᱠᱚ ᱛᱟᱞᱟ ᱨᱮ ᱯᱷᱟᱨᱪᱟ ᱯᱩᱨᱟᱹᱣ ᱮᱫᱟᱭ᱾

External links

• Quantum Cook Book Archived ᱒᱐᱒᱓-᱑᱐-᱑᱐ at the Wayback Machine. (PDF) and PHYS 201: Fundamentals of Physics II by Ramamurti Shankar, Yale OpenCourseware
• The Modern Revolution in Physics – an online textbook.
• Quantum Physics I at MIT OpenCourseWare