(1)は左辺、右辺にそれぞれ波動関数の解を代入して等しくなればよいのではないかと思ったのですが、上手くいきませんでした。

[4]一次元無限井戸型ボテンシャルのシュレディンガー方程式について以下の手順で解く。 h? ap(x) xs0,asxのとき U(x) = 0 + U(x)p(x) = Ep(x) 2m dx2 0<x<aのときU(x) = 0 このとき波動関数の解は (x) = Asink,x + Bcosk2x の形で表せることを示せ。

間違えが10個あります。 教えてください。

On July, a Japanese friend named Toshi and I decided to climb Kitadake, who is Japan's second highest mountain. Knowing this wouldn't be easy 1I started training. I went jogging and swimming regularly to trying and prepare and was feeling fit and ready at the end of July. At the beginning of August, the number of Corona cases was increasing so unfortunately we had to change our plans. Toshi doesn't want to catch the bus from Kofu to the Suothern Alps because of the risk of Corona infection, so we stayed in Shizuoka prefecture. Yanbushi was a mountain, 2014 meters high. It is not far from Umegashima, which is famous for it's hot springs. Instead of Kitadake, we climbed Yanbushi. In August 10, we woke up early and drove to the starting point. It was the day after a typhoon had passed and a beautifull, clear morning in Shizuoka city. However when we arrived, it was very cloudy and it was raining lightly. After a three and a half hour climb we arrived at the summit. It rained most of the way but it wasn't so bad under the trees and actually kept us cool. It was a challenging and rewarding experience. Ithink exploring nature is a fun, healthy and interesting way to spent your free time. T have included a photo of my climb.

英検準1級の英作文の添削をお願いします。

Date No. Topic: Agree or diogre. Pegle will depend more on self- driing.cars in the future. I disagree with the idea that pesple will depand more on self- driving cars in the future, I have two reasons to support 9 my opinion in terims of unespectod poblems and Cost. Fist. there may be some unexpected problems when we are driving 運転中(2) I think that self- diving cars are not pertect, a self-driing car. so few accidents, at leost, will happen. We can not say a り。 Safe. Aren Second, self- deiving cars Cost is higher than ordinary cars. self-driving cars are Self-dhiving cars need high quality technelogy. Materials are. differat trem ordinary cars' materials. Alse. it is very diffialt Le to make self- driving cars, 50 they costs highly, People cannit co buy them easily. For these reasons,Ithink people will not depend more on self deiviog le と Cars in the futare.

多様体の接空間に関する基底定理の証明です。g(q)=∫〜と定義した関数を微積分学の基本定理を用いながら変形してg(q)=g(0)+∑gᵢuⁱと導出するのですが、これがうまくいきません。 自分は、g(q)の式をまず両辺tで微分して、次に両辺uⁱで積分して、最後に両辺tで積分... 続きを読む

12. Theorem.If{ = (x', , x") is a coordinate system in M at p, then its coordinate vectors d, lp, …… 0,l, forma basis for the tangent space T,(M); and D= E(x) 。 i=1 for all ve T(M). Proof. By the preceding remarks we can work solely on the coordinate neighborhood of G. Since u(c) = Othere is no loss of generality in assuming ど(p) = 0eR". Shrinking W if necessary gives E(W) = {qe R":|q| < } for some 8. Ifg is a smooth function on E(W) then for each 1 <isndefine og (tq) dt du g(9) = for all qe {(W). It follows using the fundamental theorem of calculus that g= g(0) + E&,u' on (W). Thus if fe &(M), setting g = f。' yields f= f(P) + Ex on U. Applying d/ax' gives f(p) = (f /0x)(P). Thus applying the tangent vector e to the formula gives (f) = 0+ E(x'(p) + E Ap)u(x) = E(Px). ず ax Since this holds for all f e &(M), the tangent vectors v and Z Ux') d,l, are equal. It remains to show that the coordinate vectors are linearly independent. But if ) a, o.l, = 0, then application to x' yields dxi 0=24 (P) = 2q d」= 4. In particular the (vector space) dimension of T,(M) is the same as the dimension of M.

単振動のエネルギー保存則から変位を求める問題です。積分しなければいけないことはわかるのですが、どう積分したら良いかわからないので計算過程を教えてください。

エネルギー保存則 (金) から、(t) = Asin(wt + 6) を導け。 2 1 de 1 1 2mA°? dt

英検準1級のライティングをどなたか添削していただけませんか。見にくいところがあれば言ってください。よろしくお願いします。

Date No. Tapi Age or disageei People will stop subscribing to peinted. news papers in the fuature. I agre with the idea that peoplewill stop sulkstibing to printed newspapers in the tiature. I have two reasens to support my opinion. Fist it is Good for the envirenment to reduce paper. Many peaple who read nenspagers take away them they have read, s0 quantity of geboge inaease. On the other hand online news does not make garbage Also, people carn read and bring Dnline nens easier then newspapers Secand, peaple can read wlatest news on online news. Newspapers' nems is the doj's news too, but they are not latest hews, However, online news provides new news any time. It makes our lives Comvenient. It is for these reasons L think that readers of newspaper will disapear in the frnure

2階線形微分方程式の問題です。 画像2枚目のように計算したのですが、解答は正しいでしょうか？p(実数)があるため、逆三角関数を綺麗にできずに困っています。

III. z の関数y= y(z) に対する次の線形常微分方程式を考える。 (1-y dz dz? dy -+アy=0. ここでpは定数である。変数変換x= sin0 を用いて一般解 y(z) を求めよ。 IV.変数 の2次以下の多項式 f(a) 全体のなす複素線形空間をV とする。

軽く聞きたいのですが、（1）（2）は写真通りの手順で合ってますか？

6. aを正の定数とし,ベクトル関数 r= (a cos u sin v, asinusinv, a cos ) (D:0Su、 ) lidt 2. で表される曲面を考える. 次の問いに答えよ。 (1) 単位法線ベクトルを求め の端 N ON線べッ (2) 曲面の面積Sを求めよ. Alr 気、 める h dlh lder ov hadle hecda

1から9までを埋めなければならないのですが、質問の意味もよくわからず…。どなたか質問の意味と解き方を教えて頂けると助かります…！

Vocabulary skills: Collocations Read the text. Then find verbs that collocate with the words and phrases below. Write the infinitive of each verb. KEY VOCABULARY SKILLS STUDY SHEET 7, PAGE 164 The Duke of Edinburgh’'s Award The Duke of Edinburgh's Award (known as the DofE) began in the U.K. in 1956. It gives young people from all backgrounds an opportunity to experience challenge and adventure, acquire new skills, and make new friends. Each year, participants between the ages of 14 and 24 complete many hours of voluntary community work. There are three levels: Bronze, Silver, and Gold. Each one requires increasing commitment, so you can choose which level is best for you. There are four sections at Bronze and Silver level, and five at Gold. These sections combine practical, cultural, and adventurous activities. Achieving a Duke of Edinburgh's Award helps young people to develop a sense of responsibility, and promotes values of persistence, commitment, and enterprise. It has a lasting impact on young people's behavior, skils, and life chances. In 1988, the DofE was expanded to become international. These days, over 635,000 participants around the world are achieving a DofE at any one time. Since the DofE began, Over six million young people in over 123 countries have taken part, and it continues to grow in popularity. 1 an appointment / small talk / progress success / your goals / independence dark / older / crops 2 4 a course / a form / an exercise someone a chance / a talk / feedback 5 awareness / growth / competition a qualification / knowledge / a reputation for something a problem / dificulty / something at first hand a friendship / a taste for something / an idea 6 7 8 9 Predicting Look at the title of the information sheet you’re going to read. Discus with a partner what. think you'll read about. Gnbal Youth Service Day

In the new global economy brands represent a huge portion of the value of a company and, increasingly,its biggest source of profits. 上記の... 続きを読む